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[分享] 单位分数难题续

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数学星空
发表于 2010-1-18 18:21:07 | 显示全部楼层 |阅读模式

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若$x_1,x_2,....,x_n$均为正整数,且$x_1>=x_2>=x_3>=x_4....>=x_n$
求 $1/x_1+1/x_2+....+1/x_n=1\quad(5<=n<=8) $的所有解?


前面一个贴子中"关于单位分数的一些难题"中,http://bbs.emath.ac.cn/thread-2060-1-1.html
mathe出色而快速的完成了计算过程
现在,我们进一步提出上面的问题,希望能更完美的解决....
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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KeyTo9_Fans
发表于 2010-1-18 23:05:37 | 显示全部楼层
n=5太简单，写一个没有任何技术含量的基于浮点运算的穷举程序就解决了。

代码如下：
  1. #include<cstdio>
  2. #include<math.h>

  4. int a,b,c,d,g;
  5. double e[1000],f;

  7. int main()
  8. {
  9.         for(a=1;a<1000;a++)e[a]=1.0/a;
  10.         for(a=2;a<6;a++)
  11.                 for(b=a;b<9;b++)
  12.                         for(c=b;c<19;c++)
  13.                                 for(d=c;d<85;d++)
  14.                                 {
  15.                                         f=1-e[a]-e[b]-e[c]-e[d];
  16.                                         if(f>1e-9)
  17.                                         {
  18.                                                 f=1/f;
  19.                                                 g=int(f+0.5);
  20.                                                 if(g>=d&&fabs(f-g)<1e-9)
  21.                                                 {
  22.                                                         printf("1/%d + 1/%d + 1/%d + 1/%d + 1/%d = 1\n",a,b,c,d,int(f+0.5));
  23.                                                 }
  24.                                         }
  25.                                 }
  26.         return 0;
  27. }
复制代码
输出结果：
  1. 1/2 + 1/3 + 1/7 + 1/43 + 1/1806 = 1
  2. 1/2 + 1/3 + 1/7 + 1/44 + 1/924 = 1
  3. 1/2 + 1/3 + 1/7 + 1/45 + 1/630 = 1
  4. 1/2 + 1/3 + 1/7 + 1/46 + 1/483 = 1
  5. 1/2 + 1/3 + 1/7 + 1/48 + 1/336 = 1
  6. 1/2 + 1/3 + 1/7 + 1/49 + 1/294 = 1
  7. 1/2 + 1/3 + 1/7 + 1/51 + 1/238 = 1
  8. 1/2 + 1/3 + 1/7 + 1/54 + 1/189 = 1
  9. 1/2 + 1/3 + 1/7 + 1/56 + 1/168 = 1
  10. 1/2 + 1/3 + 1/7 + 1/60 + 1/140 = 1
  11. 1/2 + 1/3 + 1/7 + 1/63 + 1/126 = 1
  12. 1/2 + 1/3 + 1/7 + 1/70 + 1/105 = 1
  13. 1/2 + 1/3 + 1/7 + 1/78 + 1/91 = 1
  14. 1/2 + 1/3 + 1/7 + 1/84 + 1/84 = 1
  15. 1/2 + 1/3 + 1/8 + 1/25 + 1/600 = 1
  16. 1/2 + 1/3 + 1/8 + 1/26 + 1/312 = 1
  17. 1/2 + 1/3 + 1/8 + 1/27 + 1/216 = 1
  18. 1/2 + 1/3 + 1/8 + 1/28 + 1/168 = 1
  19. 1/2 + 1/3 + 1/8 + 1/30 + 1/120 = 1
  20. 1/2 + 1/3 + 1/8 + 1/32 + 1/96 = 1
  21. 1/2 + 1/3 + 1/8 + 1/33 + 1/88 = 1
  22. 1/2 + 1/3 + 1/8 + 1/36 + 1/72 = 1
  23. 1/2 + 1/3 + 1/8 + 1/40 + 1/60 = 1
  24. 1/2 + 1/3 + 1/8 + 1/42 + 1/56 = 1
  25. 1/2 + 1/3 + 1/8 + 1/48 + 1/48 = 1
  26. 1/2 + 1/3 + 1/9 + 1/19 + 1/342 = 1
  27. 1/2 + 1/3 + 1/9 + 1/20 + 1/180 = 1
  28. 1/2 + 1/3 + 1/9 + 1/21 + 1/126 = 1
  29. 1/2 + 1/3 + 1/9 + 1/22 + 1/99 = 1
  30. 1/2 + 1/3 + 1/9 + 1/24 + 1/72 = 1
  31. 1/2 + 1/3 + 1/9 + 1/27 + 1/54 = 1
  32. 1/2 + 1/3 + 1/9 + 1/30 + 1/45 = 1
  33. 1/2 + 1/3 + 1/9 + 1/36 + 1/36 = 1
  34. 1/2 + 1/3 + 1/10 + 1/16 + 1/240 = 1
  35. 1/2 + 1/3 + 1/10 + 1/18 + 1/90 = 1
  36. 1/2 + 1/3 + 1/10 + 1/20 + 1/60 = 1
  37. 1/2 + 1/3 + 1/10 + 1/24 + 1/40 = 1
  38. 1/2 + 1/3 + 1/10 + 1/30 + 1/30 = 1
  39. 1/2 + 1/3 + 1/11 + 1/14 + 1/231 = 1
  40. 1/2 + 1/3 + 1/11 + 1/15 + 1/110 = 1
  41. 1/2 + 1/3 + 1/11 + 1/22 + 1/33 = 1
  42. 1/2 + 1/3 + 1/12 + 1/13 + 1/156 = 1
  43. 1/2 + 1/3 + 1/12 + 1/14 + 1/84 = 1
  44. 1/2 + 1/3 + 1/12 + 1/15 + 1/60 = 1
  45. 1/2 + 1/3 + 1/12 + 1/16 + 1/48 = 1
  46. 1/2 + 1/3 + 1/12 + 1/18 + 1/36 = 1
  47. 1/2 + 1/3 + 1/12 + 1/20 + 1/30 = 1
  48. 1/2 + 1/3 + 1/12 + 1/21 + 1/28 = 1
  49. 1/2 + 1/3 + 1/12 + 1/24 + 1/24 = 1
  50. 1/2 + 1/3 + 1/13 + 1/13 + 1/78 = 1
  51. 1/2 + 1/3 + 1/14 + 1/14 + 1/42 = 1
  52. 1/2 + 1/3 + 1/14 + 1/15 + 1/35 = 1
  53. 1/2 + 1/3 + 1/14 + 1/21 + 1/21 = 1
  54. 1/2 + 1/3 + 1/15 + 1/15 + 1/30 = 1
  55. 1/2 + 1/3 + 1/15 + 1/20 + 1/20 = 1
  56. 1/2 + 1/3 + 1/16 + 1/16 + 1/24 = 1
  57. 1/2 + 1/3 + 1/18 + 1/18 + 1/18 = 1
  58. 1/2 + 1/4 + 1/5 + 1/21 + 1/420 = 1
  59. 1/2 + 1/4 + 1/5 + 1/22 + 1/220 = 1
  60. 1/2 + 1/4 + 1/5 + 1/24 + 1/120 = 1
  61. 1/2 + 1/4 + 1/5 + 1/25 + 1/100 = 1
  62. 1/2 + 1/4 + 1/5 + 1/28 + 1/70 = 1
  63. 1/2 + 1/4 + 1/5 + 1/30 + 1/60 = 1
  64. 1/2 + 1/4 + 1/5 + 1/36 + 1/45 = 1
  65. 1/2 + 1/4 + 1/5 + 1/40 + 1/40 = 1
  66. 1/2 + 1/4 + 1/6 + 1/13 + 1/156 = 1
  67. 1/2 + 1/4 + 1/6 + 1/14 + 1/84 = 1
  68. 1/2 + 1/4 + 1/6 + 1/15 + 1/60 = 1
  69. 1/2 + 1/4 + 1/6 + 1/16 + 1/48 = 1
  70. 1/2 + 1/4 + 1/6 + 1/18 + 1/36 = 1
  71. 1/2 + 1/4 + 1/6 + 1/20 + 1/30 = 1
  72. 1/2 + 1/4 + 1/6 + 1/21 + 1/28 = 1
  73. 1/2 + 1/4 + 1/6 + 1/24 + 1/24 = 1
  74. 1/2 + 1/4 + 1/7 + 1/10 + 1/140 = 1
  75. 1/2 + 1/4 + 1/7 + 1/12 + 1/42 = 1
  76. 1/2 + 1/4 + 1/7 + 1/14 + 1/28 = 1
  77. 1/2 + 1/4 + 1/8 + 1/9 + 1/72 = 1
  78. 1/2 + 1/4 + 1/8 + 1/10 + 1/40 = 1
  79. 1/2 + 1/4 + 1/8 + 1/12 + 1/24 = 1
  80. 1/2 + 1/4 + 1/8 + 1/16 + 1/16 = 1
  81. 1/2 + 1/4 + 1/9 + 1/9 + 1/36 = 1
  82. 1/2 + 1/4 + 1/9 + 1/12 + 1/18 = 1
  83. 1/2 + 1/4 + 1/10 + 1/10 + 1/20 = 1
  84. 1/2 + 1/4 + 1/10 + 1/12 + 1/15 = 1
  85. 1/2 + 1/4 + 1/12 + 1/12 + 1/12 = 1
  86. 1/2 + 1/5 + 1/5 + 1/11 + 1/110 = 1
  87. 1/2 + 1/5 + 1/5 + 1/12 + 1/60 = 1
  88. 1/2 + 1/5 + 1/5 + 1/14 + 1/35 = 1
  89. 1/2 + 1/5 + 1/5 + 1/15 + 1/30 = 1
  90. 1/2 + 1/5 + 1/5 + 1/20 + 1/20 = 1
  91. 1/2 + 1/5 + 1/6 + 1/8 + 1/120 = 1
  92. 1/2 + 1/5 + 1/6 + 1/9 + 1/45 = 1
  93. 1/2 + 1/5 + 1/6 + 1/10 + 1/30 = 1
  94. 1/2 + 1/5 + 1/6 + 1/12 + 1/20 = 1
  95. 1/2 + 1/5 + 1/6 + 1/15 + 1/15 = 1
  96. 1/2 + 1/5 + 1/7 + 1/7 + 1/70 = 1
  97. 1/2 + 1/5 + 1/8 + 1/8 + 1/20 = 1
  98. 1/2 + 1/5 + 1/10 + 1/10 + 1/10 = 1
  99. 1/2 + 1/6 + 1/6 + 1/7 + 1/42 = 1
  100. 1/2 + 1/6 + 1/6 + 1/8 + 1/24 = 1
  101. 1/2 + 1/6 + 1/6 + 1/9 + 1/18 = 1
  102. 1/2 + 1/6 + 1/6 + 1/10 + 1/15 = 1
  103. 1/2 + 1/6 + 1/6 + 1/12 + 1/12 = 1
  104. 1/2 + 1/6 + 1/7 + 1/7 + 1/21 = 1
  105. 1/2 + 1/6 + 1/8 + 1/8 + 1/12 = 1
  106. 1/2 + 1/6 + 1/9 + 1/9 + 1/9 = 1
  107. 1/2 + 1/7 + 1/7 + 1/7 + 1/14 = 1
  108. 1/2 + 1/8 + 1/8 + 1/8 + 1/8 = 1
  109. 1/3 + 1/3 + 1/4 + 1/13 + 1/156 = 1
  110. 1/3 + 1/3 + 1/4 + 1/14 + 1/84 = 1
  111. 1/3 + 1/3 + 1/4 + 1/15 + 1/60 = 1
  112. 1/3 + 1/3 + 1/4 + 1/16 + 1/48 = 1
  113. 1/3 + 1/3 + 1/4 + 1/18 + 1/36 = 1
  114. 1/3 + 1/3 + 1/4 + 1/20 + 1/30 = 1
  115. 1/3 + 1/3 + 1/4 + 1/21 + 1/28 = 1
  116. 1/3 + 1/3 + 1/4 + 1/24 + 1/24 = 1
  117. 1/3 + 1/3 + 1/5 + 1/8 + 1/120 = 1
  118. 1/3 + 1/3 + 1/5 + 1/9 + 1/45 = 1
  119. 1/3 + 1/3 + 1/5 + 1/10 + 1/30 = 1
  120. 1/3 + 1/3 + 1/5 + 1/12 + 1/20 = 1
  121. 1/3 + 1/3 + 1/5 + 1/15 + 1/15 = 1
  122. 1/3 + 1/3 + 1/6 + 1/7 + 1/42 = 1
  123. 1/3 + 1/3 + 1/6 + 1/8 + 1/24 = 1
  124. 1/3 + 1/3 + 1/6 + 1/9 + 1/18 = 1
  125. 1/3 + 1/3 + 1/6 + 1/10 + 1/15 = 1
  126. 1/3 + 1/3 + 1/6 + 1/12 + 1/12 = 1
  127. 1/3 + 1/3 + 1/7 + 1/7 + 1/21 = 1
  128. 1/3 + 1/3 + 1/8 + 1/8 + 1/12 = 1
  129. 1/3 + 1/3 + 1/9 + 1/9 + 1/9 = 1
  130. 1/3 + 1/4 + 1/4 + 1/7 + 1/42 = 1
  131. 1/3 + 1/4 + 1/4 + 1/8 + 1/24 = 1
  132. 1/3 + 1/4 + 1/4 + 1/9 + 1/18 = 1
  133. 1/3 + 1/4 + 1/4 + 1/10 + 1/15 = 1
  134. 1/3 + 1/4 + 1/4 + 1/12 + 1/12 = 1
  135. 1/3 + 1/4 + 1/5 + 1/5 + 1/60 = 1
  136. 1/3 + 1/4 + 1/5 + 1/6 + 1/20 = 1
  137. 1/3 + 1/4 + 1/6 + 1/6 + 1/12 = 1
  138. 1/3 + 1/4 + 1/6 + 1/8 + 1/8 = 1
  139. 1/3 + 1/5 + 1/5 + 1/5 + 1/15 = 1
  140. 1/3 + 1/5 + 1/5 + 1/6 + 1/10 = 1
  141. 1/3 + 1/6 + 1/6 + 1/6 + 1/6 = 1
  142. 1/4 + 1/4 + 1/4 + 1/5 + 1/20 = 1
  143. 1/4 + 1/4 + 1/4 + 1/6 + 1/12 = 1
  144. 1/4 + 1/4 + 1/4 + 1/8 + 1/8 = 1
  145. 1/4 + 1/4 + 1/5 + 1/5 + 1/10 = 1
  146. 1/4 + 1/4 + 1/6 + 1/6 + 1/6 = 1
  147. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1
复制代码
枚举量：21549
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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数学星空
 楼主| 发表于 2010-1-19 08:21:53 | 显示全部楼层
呵呵,对于n=5,利用Wayne提供的程序也就几分钟时间
111.jpg
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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mathe
发表于 2010-1-19 08:43:10 | 显示全部楼层
对于n=8,应该可以穷举6个数,后面两个数通过解方程方法来得出.只是总数会有点多.
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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medie2005
发表于 2010-1-19 08:53:17 | 显示全部楼层
要搜索的话，先找一下约束关系吧。
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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mathe
发表于 2010-1-19 09:07:34 | 显示全部楼层
稍微修改一下前面的gp程序就可以了.不过运算结果标明处理N=7还行,但是N=8估计解太多了,全部求解可能性不大,看来应该改成以计数作为目标.
其中N=6的解总数为2060
N=7还在运行中,有点慢

  2. N()=
  3. {
  4.   7
  5. }

  7. K()=
  8. {
  9.     N()-2
  10. }

  12. BEGIN()=
  13. {
  14.     0
  15. }

  17. END()=
  18. {
  19.     -1
  20. }

  22. OUTFILENAME()=
  23. {
  24.     "N7.txt"
  25. }

  27. output()=
  28. {
  29.     local(V,MM,RR,uu,f,v,v2,a,b,d);
  30.     MM=M[K()];
  31.     RR=R[K()];
  32.     V=MM;
  33.     c=c+1;
  34.     if(c>=BEGIN()&&(END()<0||c<=END()),
  35.             f=divisors(V);
  36.             for(u=1,length(f),
  37.               for(u2=u+1,length(f),
  38.                 v=f[u];v2=f[u2];
  39.                 if((v+v2)%RR!=0, next());
  40.                 if(gcd(v,v2)>1,next());
  41.                 d=(v+v2)/RR*(V/(v*v2));
  42.                 a=d*v;b=d*v2;
  43.                 if(a>n[K()],
  44.                        n[K()+1]=a;
  45.                        n[K()+2]=b;
  46.                        write(OUTFILENAME(),n)
  47.                 )
  48.               )
  49.             )
  50.     );
  51.     if(c%100==0, print("process " c " lines"))
  52. }

  54. search(level)=
  55. {
  56.     local(ll,uu,dd);
  57.     if(level>=K(),
  58.        output(),
  59.        ll=floor(M[level]/R[level])+1;
  60.        uu=floor((N()-level)*M[level]/R[level]);
  61.        if(ll<=n[level],ll=n[level]+1);
  62.        for(i=ll,uu,
  63.           n[level+1]=i;
  64.           dd=gcd(M[level],i);
  65.           M[level+1]=M[level]*i/dd;
  66.           R[level+1]=(R[level]*i-M[level])/dd;
  67.           A[i%4+1]=A[i%4+1]+1;
  68.           search(level+1);
  69.           A[i%4+1]=A[i%4+1]-1
  70.        )
  71.     )
  72. }

  74. search0()=
  75. {
  76.    n=vector(N());
  77.    M=vector(N());
  78.    R=vector(N());
  79.    A=vector(4);
  80.    c=0;
  81.    for(i=2,7,
  82.       n[1]=i;
  83.       R[1]=i-1;
  84.       M[1]=i;
  85.       A[i%4+1]=A[i%4+1]+1;
  86.       search(1);
  87.       A[i%4+1]=A[i%4+1]-1;
  88.    )
  89. }
复制代码
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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mathe
发表于 2010-1-19 09:11:41 | 显示全部楼层
发现N=5时同KeyTo9_Fans结果不一致,才发现这里允许重复的数据,那么代码还得修改一下:

  2. N()=
  3. {
  4.   5
  5. }

  7. K()=
  8. {
  9.     N()-2
  10. }

  12. BEGIN()=
  13. {
  14.     0
  15. }

  17. END()=
  18. {
  19.     -1
  20. }

  22. OUTFILENAME()=
  23. {
  24.     "/home/zdu/N5.txt"
  25. }

  27. output()=
  28. {
  29.     local(V,MM,RR,uu,f,v,v2,a,b,d);
  30.     MM=M[K()];
  31.     RR=R[K()];
  32.     V=MM;
  33.     c=c+1;
  34.     if(c>=BEGIN()&&(END()<0||c<=END()),
  35.             f=divisors(V);
  36.             for(u=1,length(f),
  37.               for(u2=u+1,length(f),
  38.                 v=f[u];v2=f[u2];
  39.                 if((v+v2)%RR!=0, next());
  40.                 if(gcd(v,v2)>1,next());
  41.                 d=(v+v2)/RR*(V/(v*v2));
  42.                 a=d*v;b=d*v2;
  43.                 if(a>n[K()],
  44.                        n[K()+1]=a;
  45.                        n[K()+2]=b;
  46.                        write(OUTFILENAME(),n)
  47.                 )
  48.               )
  49.             )
  50.     );
  51.     if(c%100==0, print("process " c " lines"))
  52. }

  54. search(level)=
  55. {
  56.     local(ll,uu,dd);
  57.     if(level>=K(),
  58.        output(),
  59.        ll=floor(M[level]/R[level])+1;
  60.        uu=floor((N()-level)*M[level]/R[level]);
  61.        if(ll<=n[level],ll=n[level]);
  62.        for(i=ll,uu,
  63.           n[level+1]=i;
  64.           dd=gcd(M[level],i);
  65.           M[level+1]=M[level]*i/dd;
  66.           R[level+1]=(R[level]*i-M[level])/dd;
  67.           A[i%4+1]=A[i%4+1]+1;
  68.           search(level+1);
  69.           A[i%4+1]=A[i%4+1]-1
  70.        )
  71.     )
  72. }

  74. search0()=
  75. {
  76.    n=vector(N());
  77.    M=vector(N());
  78.    R=vector(N());
  79.    A=vector(4);
  80.    c=0;
  81.    for(i=2,8,
  82.       n[1]=i;
  83.       R[1]=i-1;
  84.       M[1]=i;
  85.       A[i%4+1]=A[i%4+1]+1;
  86.       search(1);
  87.       A[i%4+1]=A[i%4+1]-1;
  88.    )
  89. }
复制代码
结果N=5有167个

  2. [2, 3, 7, 63, 126]
  3. [2, 3, 7, 56, 168]
  4. [2, 3, 7, 49, 294]
  5. [2, 3, 7, 48, 336]
  6. [2, 3, 7, 45, 630]
  7. [2, 3, 7, 44, 924]
  8. [2, 3, 7, 43, 1806]
  9. [2, 3, 7, 70, 105]
  10. [2, 3, 7, 54, 189]
  11. [2, 3, 7, 46, 483]
  12. [2, 3, 7, 60, 140]
  13. [2, 3, 7, 51, 238]
  14. [2, 3, 7, 78, 91]
  15. [2, 3, 8, 36, 72]
  16. [2, 3, 8, 32, 96]
  17. [2, 3, 8, 30, 120]
  18. [2, 3, 8, 28, 168]
  19. [2, 3, 8, 27, 216]
  20. [2, 3, 8, 26, 312]
  21. [2, 3, 8, 25, 600]
  22. [2, 3, 8, 40, 60]
  23. [2, 3, 8, 42, 56]
  24. [2, 3, 8, 33, 88]
  25. [2, 3, 9, 27, 54]
  26. [2, 3, 9, 24, 72]
  27. [2, 3, 9, 21, 126]
  28. [2, 3, 9, 20, 180]
  29. [2, 3, 9, 19, 342]
  30. [2, 3, 9, 30, 45]
  31. [2, 3, 9, 22, 99]
  32. [2, 3, 10, 20, 60]
  33. [2, 3, 10, 18, 90]
  34. [2, 3, 10, 16, 240]
  35. [2, 3, 10, 24, 40]
  36. [2, 3, 11, 22, 33]
  37. [2, 3, 11, 14, 231]
  38. [2, 3, 11, 15, 110]
  39. [2, 3, 12, 18, 36]
  40. [2, 3, 12, 16, 48]
  41. [2, 3, 12, 15, 60]
  42. [2, 3, 12, 14, 84]
  43. [2, 3, 12, 13, 156]
  44. [2, 3, 12, 20, 30]
  45. [2, 3, 12, 21, 28]
  46. [2, 4, 5, 30, 60]
  47. [2, 4, 5, 25, 100]
  48. [2, 4, 5, 24, 120]
  49. [2, 4, 5, 22, 220]
  50. [2, 4, 5, 21, 420]
  51. [2, 4, 5, 28, 70]
  52. [2, 4, 5, 36, 45]
  53. [2, 4, 6, 18, 36]
  54. [2, 4, 6, 16, 48]
  55. [2, 4, 6, 15, 60]
  56. [2, 4, 6, 14, 84]
  57. [2, 4, 6, 13, 156]
  58. [2, 4, 6, 20, 30]
  59. [2, 4, 6, 21, 28]
  60. [2, 4, 7, 14, 28]
  61. [2, 4, 7, 10, 140]
  62. [2, 4, 7, 12, 42]
  63. [2, 4, 8, 12, 24]
  64. [2, 4, 8, 10, 40]
  65. [2, 4, 8, 9, 72]
  66. [2, 4, 9, 12, 18]
  67. [2, 4, 10, 12, 15]
  68. [2, 5, 6, 10, 30]
  69. [2, 5, 6, 8, 120]
  70. [2, 5, 6, 12, 20]
  71. [3, 4, 5, 6, 20]
  72. [2, 3, 7, 63, 126]
  73. [2, 3, 7, 56, 168]
  74. [2, 3, 7, 49, 294]
  75. [2, 3, 7, 48, 336]
  76. [2, 3, 7, 45, 630]
  77. [2, 3, 7, 44, 924]
  78. [2, 3, 7, 43, 1806]
  79. [2, 3, 7, 70, 105]
  80. [2, 3, 7, 54, 189]
  81. [2, 3, 7, 46, 483]
  82. [2, 3, 7, 60, 140]
  83. [2, 3, 7, 51, 238]
  84. [2, 3, 7, 78, 91]
  85. [2, 3, 8, 36, 72]
  86. [2, 3, 8, 32, 96]
  87. [2, 3, 8, 30, 120]
  88. [2, 3, 8, 28, 168]
  89. [2, 3, 8, 27, 216]
  90. [2, 3, 8, 26, 312]
  91. [2, 3, 8, 25, 600]
  92. [2, 3, 8, 40, 60]
  93. [2, 3, 8, 42, 56]
  94. [2, 3, 8, 33, 88]
  95. [2, 3, 9, 27, 54]
  96. [2, 3, 9, 24, 72]
  97. [2, 3, 9, 21, 126]
  98. [2, 3, 9, 20, 180]
  99. [2, 3, 9, 19, 342]
  100. [2, 3, 9, 30, 45]
  101. [2, 3, 9, 22, 99]
  102. [2, 3, 10, 20, 60]
  103. [2, 3, 10, 18, 90]
  104. [2, 3, 10, 16, 240]
  105. [2, 3, 10, 24, 40]
  106. [2, 3, 11, 22, 33]
  107. [2, 3, 11, 14, 231]
  108. [2, 3, 11, 15, 110]
  109. [2, 3, 12, 18, 36]
  110. [2, 3, 12, 16, 48]
  111. [2, 3, 12, 15, 60]
  112. [2, 3, 12, 14, 84]
  113. [2, 3, 12, 13, 156]
  114. [2, 3, 12, 20, 30]
  115. [2, 3, 12, 21, 28]
  116. [2, 4, 5, 30, 60]
  117. [2, 4, 5, 25, 100]
  118. [2, 4, 5, 24, 120]
  119. [2, 4, 5, 22, 220]
  120. [2, 4, 5, 21, 420]
  121. [2, 4, 5, 28, 70]
  122. [2, 4, 5, 36, 45]
  123. [2, 4, 6, 18, 36]
  124. [2, 4, 6, 16, 48]
  125. [2, 4, 6, 15, 60]
  126. [2, 4, 6, 14, 84]
  127. [2, 4, 6, 13, 156]
  128. [2, 4, 6, 20, 30]
  129. [2, 4, 6, 21, 28]
  130. [2, 4, 7, 14, 28]
  131. [2, 4, 7, 10, 140]
  132. [2, 4, 7, 12, 42]
  133. [2, 4, 8, 12, 24]
  134. [2, 4, 8, 10, 40]
  135. [2, 4, 8, 9, 72]
  136. [2, 4, 9, 12, 18]
  137. [2, 4, 10, 12, 15]
  138. [2, 5, 5, 15, 30]
  139. [2, 5, 5, 12, 60]
  140. [2, 5, 5, 11, 110]
  141. [2, 5, 5, 14, 35]
  142. [2, 5, 6, 10, 30]
  143. [2, 5, 6, 8, 120]
  144. [2, 5, 6, 12, 20]
  145. [2, 6, 6, 9, 18]
  146. [2, 6, 6, 8, 24]
  147. [2, 6, 6, 7, 42]
  148. [2, 6, 6, 10, 15]
  149. [3, 3, 4, 18, 36]
  150. [3, 3, 4, 16, 48]
  151. [3, 3, 4, 15, 60]
  152. [3, 3, 4, 14, 84]
  153. [3, 3, 4, 13, 156]
  154. [3, 3, 4, 20, 30]
  155. [3, 3, 4, 21, 28]
  156. [3, 3, 5, 10, 30]
  157. [3, 3, 5, 9, 45]
  158. [3, 3, 5, 8, 120]
  159. [3, 3, 5, 12, 20]
  160. [3, 3, 6, 9, 18]
  161. [3, 3, 6, 8, 24]
  162. [3, 3, 6, 7, 42]
  163. [3, 3, 6, 10, 15]
  164. [3, 4, 4, 8, 24]
  165. [3, 4, 5, 6, 20]
  166. [3, 5, 5, 6, 10]
  167. [4, 4, 4, 6, 12]
  168. [4, 4, 4, 5, 20]
复制代码
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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mathe
发表于 2010-1-19 09:18:37 | 显示全部楼层
修改bug:

  2. N()=
  3. {
  4.   5
  5. }

  7. K()=
  8. {
  9.     N()-2
  10. }

  12. BEGIN()=
  13. {
  14.     0
  15. }

  17. END()=
  18. {
  19.     -1
  20. }

  22. OUTFILENAME()=
  23. {
  24.     "/home/zdu/N5.txt"
  25. }

  27. output()=
  28. {
  29.     local(V,MM,RR,uu,f,v,v2,a,b,d);
  30.     MM=M[K()];
  31.     RR=R[K()];
  32.     V=MM;
  33.     c=c+1;
  34.     if(c>=BEGIN()&&(END()<0||c<=END()),
  35.             f=divisors(V);
  36.             for(u=1,length(f),
  37.               for(u2=u,length(f),
  38.                 v=f[u];v2=f[u2];
  39.                 if((v+v2)%RR!=0, next());
  40.                 if(gcd(v,v2)>1,next());
  41.                 d=(v+v2)/RR*(V/(v*v2));
  42.                 a=d*v;b=d*v2;
  43.                 if(a>=n[K()],
  44.                        n[K()+1]=a;
  45.                        n[K()+2]=b;
  46.                        write(OUTFILENAME(),n)
  47.                 )
  48.               )
  49.             )
  50.     );
  51.     if(c%100==0, print("process " c " lines"))
  52. }

  54. search(level)=
  55. {
  56.     local(ll,uu,dd);
  57.     if(level>=K(),
  58.        output(),
  59.        ll=floor(M[level]/R[level])+1;
  60.        uu=floor((N()-level)*M[level]/R[level]);
  61.        if(ll<=n[level],ll=n[level]);
  62.        for(i=ll,uu,
  63.           n[level+1]=i;
  64.           dd=gcd(M[level],i);
  65.           M[level+1]=M[level]*i/dd;
  66.           R[level+1]=(R[level]*i-M[level])/dd;
  67.           A[i%4+1]=A[i%4+1]+1;
  68.           search(level+1);
  69.           A[i%4+1]=A[i%4+1]-1
  70.        )
  71.     )
  72. }

  74. search0()=
  75. {
  76.    n=vector(N());
  77.    M=vector(N());
  78.    R=vector(N());
  79.    A=vector(4);
  80.    c=0;
  81.    for(i=2,8,
  82.       n[1]=i;
  83.       R[1]=i-1;
  84.       M[1]=i;
  85.       A[i%4+1]=A[i%4+1]+1;
  86.       search(1);
  87.       A[i%4+1]=A[i%4+1]-1;
  88.    )
  89. }
复制代码
N=5的结果很多,有413个

  2. [2, 3, 7, 63, 126]
  3. [2, 3, 7, 56, 168]
  4. [2, 3, 7, 49, 294]
  5. [2, 3, 7, 48, 336]
  6. [2, 3, 7, 45, 630]
  7. [2, 3, 7, 44, 924]
  8. [2, 3, 7, 43, 1806]
  9. [2, 3, 7, 70, 105]
  10. [2, 3, 7, 54, 189]
  11. [2, 3, 7, 46, 483]
  12. [2, 3, 7, 60, 140]
  13. [2, 3, 7, 51, 238]
  14. [2, 3, 7, 78, 91]
  15. [2, 3, 8, 36, 72]
  16. [2, 3, 8, 32, 96]
  17. [2, 3, 8, 30, 120]
  18. [2, 3, 8, 28, 168]
  19. [2, 3, 8, 27, 216]
  20. [2, 3, 8, 26, 312]
  21. [2, 3, 8, 25, 600]
  22. [2, 3, 8, 40, 60]
  23. [2, 3, 8, 42, 56]
  24. [2, 3, 8, 33, 88]
  25. [2, 3, 9, 27, 54]
  26. [2, 3, 9, 24, 72]
  27. [2, 3, 9, 21, 126]
  28. [2, 3, 9, 20, 180]
  29. [2, 3, 9, 19, 342]
  30. [2, 3, 9, 30, 45]
  31. [2, 3, 9, 22, 99]
  32. [2, 3, 10, 20, 60]
  33. [2, 3, 10, 18, 90]
  34. [2, 3, 10, 16, 240]
  35. [2, 3, 10, 24, 40]
  36. [2, 3, 11, 22, 33]
  37. [2, 3, 11, 14, 231]
  38. [2, 3, 11, 15, 110]
  39. [2, 3, 12, 18, 36]
  40. [2, 3, 12, 16, 48]
  41. [2, 3, 12, 15, 60]
  42. [2, 3, 12, 14, 84]
  43. [2, 3, 12, 13, 156]
  44. [2, 3, 12, 20, 30]
  45. [2, 3, 12, 21, 28]
  46. [2, 4, 5, 30, 60]
  47. [2, 4, 5, 25, 100]
  48. [2, 4, 5, 24, 120]
  49. [2, 4, 5, 22, 220]
  50. [2, 4, 5, 21, 420]
  51. [2, 4, 5, 28, 70]
  52. [2, 4, 5, 36, 45]
  53. [2, 4, 6, 18, 36]
  54. [2, 4, 6, 16, 48]
  55. [2, 4, 6, 15, 60]
  56. [2, 4, 6, 14, 84]
  57. [2, 4, 6, 13, 156]
  58. [2, 4, 6, 20, 30]
  59. [2, 4, 6, 21, 28]
  60. [2, 4, 7, 14, 28]
  61. [2, 4, 7, 10, 140]
  62. [2, 4, 7, 12, 42]
  63. [2, 4, 8, 12, 24]
  64. [2, 4, 8, 10, 40]
  65. [2, 4, 8, 9, 72]
  66. [2, 4, 9, 12, 18]
  67. [2, 4, 10, 12, 15]
  68. [2, 5, 6, 10, 30]
  69. [2, 5, 6, 8, 120]
  70. [2, 5, 6, 12, 20]
  71. [3, 4, 5, 6, 20]
  72. [2, 3, 7, 63, 126]
  73. [2, 3, 7, 56, 168]
  74. [2, 3, 7, 49, 294]
  75. [2, 3, 7, 48, 336]
  76. [2, 3, 7, 45, 630]
  77. [2, 3, 7, 44, 924]
  78. [2, 3, 7, 43, 1806]
  79. [2, 3, 7, 70, 105]
  80. [2, 3, 7, 54, 189]
  81. [2, 3, 7, 46, 483]
  82. [2, 3, 7, 60, 140]
  83. [2, 3, 7, 51, 238]
  84. [2, 3, 7, 78, 91]
  85. [2, 3, 8, 36, 72]
  86. [2, 3, 8, 32, 96]
  87. [2, 3, 8, 30, 120]
  88. [2, 3, 8, 28, 168]
  89. [2, 3, 8, 27, 216]
  90. [2, 3, 8, 26, 312]
  91. [2, 3, 8, 25, 600]
  92. [2, 3, 8, 40, 60]
  93. [2, 3, 8, 42, 56]
  94. [2, 3, 8, 33, 88]
  95. [2, 3, 9, 27, 54]
  96. [2, 3, 9, 24, 72]
  97. [2, 3, 9, 21, 126]
  98. [2, 3, 9, 20, 180]
  99. [2, 3, 9, 19, 342]
  100. [2, 3, 9, 30, 45]
  101. [2, 3, 9, 22, 99]
  102. [2, 3, 10, 20, 60]
  103. [2, 3, 10, 18, 90]
  104. [2, 3, 10, 16, 240]
  105. [2, 3, 10, 24, 40]
  106. [2, 3, 11, 22, 33]
  107. [2, 3, 11, 14, 231]
  108. [2, 3, 11, 15, 110]
  109. [2, 3, 12, 18, 36]
  110. [2, 3, 12, 16, 48]
  111. [2, 3, 12, 15, 60]
  112. [2, 3, 12, 14, 84]
  113. [2, 3, 12, 13, 156]
  114. [2, 3, 12, 20, 30]
  115. [2, 3, 12, 21, 28]
  116. [2, 4, 5, 30, 60]
  117. [2, 4, 5, 25, 100]
  118. [2, 4, 5, 24, 120]
  119. [2, 4, 5, 22, 220]
  120. [2, 4, 5, 21, 420]
  121. [2, 4, 5, 28, 70]
  122. [2, 4, 5, 36, 45]
  123. [2, 4, 6, 18, 36]
  124. [2, 4, 6, 16, 48]
  125. [2, 4, 6, 15, 60]
  126. [2, 4, 6, 14, 84]
  127. [2, 4, 6, 13, 156]
  128. [2, 4, 6, 20, 30]
  129. [2, 4, 6, 21, 28]
  130. [2, 4, 7, 14, 28]
  131. [2, 4, 7, 10, 140]
  132. [2, 4, 7, 12, 42]
  133. [2, 4, 8, 12, 24]
  134. [2, 4, 8, 10, 40]
  135. [2, 4, 8, 9, 72]
  136. [2, 4, 9, 12, 18]
  137. [2, 4, 10, 12, 15]
  138. [2, 5, 5, 15, 30]
  139. [2, 5, 5, 12, 60]
  140. [2, 5, 5, 11, 110]
  141. [2, 5, 5, 14, 35]
  142. [2, 5, 6, 10, 30]
  143. [2, 5, 6, 8, 120]
  144. [2, 5, 6, 12, 20]
  145. [2, 6, 6, 9, 18]
  146. [2, 6, 6, 8, 24]
  147. [2, 6, 6, 7, 42]
  148. [2, 6, 6, 10, 15]
  149. [3, 3, 4, 18, 36]
  150. [3, 3, 4, 16, 48]
  151. [3, 3, 4, 15, 60]
  152. [3, 3, 4, 14, 84]
  153. [3, 3, 4, 13, 156]
  154. [3, 3, 4, 20, 30]
  155. [3, 3, 4, 21, 28]
  156. [3, 3, 5, 10, 30]
  157. [3, 3, 5, 9, 45]
  158. [3, 3, 5, 8, 120]
  159. [3, 3, 5, 12, 20]
  160. [3, 3, 6, 9, 18]
  161. [3, 3, 6, 8, 24]
  162. [3, 3, 6, 7, 42]
  163. [3, 3, 6, 10, 15]
  164. [3, 4, 4, 8, 24]
  165. [3, 4, 5, 6, 20]
  166. [3, 5, 5, 6, 10]
  167. [4, 4, 4, 6, 12]
  168. [4, 4, 4, 5, 20]
  169. [2, 3, 7, 84, 84]
  170. [2, 3, 7, 63, 126]
  171. [2, 3, 7, 56, 168]
  172. [2, 3, 7, 49, 294]
  173. [2, 3, 7, 48, 336]
  174. [2, 3, 7, 45, 630]
  175. [2, 3, 7, 44, 924]
  176. [2, 3, 7, 43, 1806]
  177. [2, 3, 7, 70, 105]
  178. [2, 3, 7, 54, 189]
  179. [2, 3, 7, 46, 483]
  180. [2, 3, 7, 60, 140]
  181. [2, 3, 7, 51, 238]
  182. [2, 3, 7, 78, 91]
  183. [2, 3, 8, 48, 48]
  184. [2, 3, 8, 36, 72]
  185. [2, 3, 8, 32, 96]
  186. [2, 3, 8, 30, 120]
  187. [2, 3, 8, 28, 168]
  188. [2, 3, 8, 27, 216]
  189. [2, 3, 8, 26, 312]
  190. [2, 3, 8, 25, 600]
  191. [2, 3, 8, 40, 60]
  192. [2, 3, 8, 42, 56]
  193. [2, 3, 8, 33, 88]
  194. [2, 3, 9, 36, 36]
  195. [2, 3, 9, 27, 54]
  196. [2, 3, 9, 24, 72]
  197. [2, 3, 9, 21, 126]
  198. [2, 3, 9, 20, 180]
  199. [2, 3, 9, 19, 342]
  200. [2, 3, 9, 30, 45]
  201. [2, 3, 9, 22, 99]
  202. [2, 3, 10, 30, 30]
  203. [2, 3, 10, 20, 60]
  204. [2, 3, 10, 18, 90]
  205. [2, 3, 10, 16, 240]
  206. [2, 3, 10, 24, 40]
  207. [2, 3, 11, 22, 33]
  208. [2, 3, 11, 14, 231]
  209. [2, 3, 11, 15, 110]
  210. [2, 3, 12, 24, 24]
  211. [2, 3, 12, 18, 36]
  212. [2, 3, 12, 16, 48]
  213. [2, 3, 12, 15, 60]
  214. [2, 3, 12, 14, 84]
  215. [2, 3, 12, 13, 156]
  216. [2, 3, 12, 20, 30]
  217. [2, 3, 12, 21, 28]
  218. [2, 4, 5, 40, 40]
  219. [2, 4, 5, 30, 60]
  220. [2, 4, 5, 25, 100]
  221. [2, 4, 5, 24, 120]
  222. [2, 4, 5, 22, 220]
  223. [2, 4, 5, 21, 420]
  224. [2, 4, 5, 28, 70]
  225. [2, 4, 5, 36, 45]
  226. [2, 4, 6, 24, 24]
  227. [2, 4, 6, 18, 36]
  228. [2, 4, 6, 16, 48]
  229. [2, 4, 6, 15, 60]
  230. [2, 4, 6, 14, 84]
  231. [2, 4, 6, 13, 156]
  232. [2, 4, 6, 20, 30]
  233. [2, 4, 6, 21, 28]
  234. [2, 4, 7, 14, 28]
  235. [2, 4, 7, 10, 140]
  236. [2, 4, 7, 12, 42]
  237. [2, 4, 8, 16, 16]
  238. [2, 4, 8, 12, 24]
  239. [2, 4, 8, 10, 40]
  240. [2, 4, 8, 9, 72]
  241. [2, 4, 9, 12, 18]
  242. [2, 4, 10, 12, 15]
  243. [2, 5, 5, 20, 20]
  244. [2, 5, 5, 15, 30]
  245. [2, 5, 5, 12, 60]
  246. [2, 5, 5, 11, 110]
  247. [2, 5, 5, 14, 35]
  248. [2, 5, 6, 10, 30]
  249. [2, 5, 6, 8, 120]
  250. [2, 5, 6, 12, 20]
  251. [2, 6, 6, 12, 12]
  252. [2, 6, 6, 9, 18]
  253. [2, 6, 6, 8, 24]
  254. [2, 6, 6, 7, 42]
  255. [2, 6, 6, 10, 15]
  256. [3, 3, 4, 24, 24]
  257. [3, 3, 4, 18, 36]
  258. [3, 3, 4, 16, 48]
  259. [3, 3, 4, 15, 60]
  260. [3, 3, 4, 14, 84]
  261. [3, 3, 4, 13, 156]
  262. [3, 3, 4, 20, 30]
  263. [3, 3, 4, 21, 28]
  264. [3, 3, 5, 15, 15]
  265. [3, 3, 5, 10, 30]
  266. [3, 3, 5, 9, 45]
  267. [3, 3, 5, 8, 120]
  268. [3, 3, 5, 12, 20]
  269. [3, 3, 6, 12, 12]
  270. [3, 3, 6, 9, 18]
  271. [3, 3, 6, 8, 24]
  272. [3, 3, 6, 7, 42]
  273. [3, 3, 6, 10, 15]
  274. [3, 4, 4, 12, 12]
  275. [3, 4, 4, 8, 24]
  276. [3, 4, 5, 6, 20]
  277. [3, 5, 5, 6, 10]
  278. [4, 4, 4, 8, 8]
  279. [4, 4, 4, 6, 12]
  280. [4, 4, 4, 5, 20]
  281. [2, 3, 7, 84, 84]
  282. [2, 3, 7, 63, 126]
  283. [2, 3, 7, 56, 168]
  284. [2, 3, 7, 49, 294]
  285. [2, 3, 7, 48, 336]
  286. [2, 3, 7, 45, 630]
  287. [2, 3, 7, 44, 924]
  288. [2, 3, 7, 43, 1806]
  289. [2, 3, 7, 70, 105]
  290. [2, 3, 7, 54, 189]
  291. [2, 3, 7, 46, 483]
  292. [2, 3, 7, 60, 140]
  293. [2, 3, 7, 51, 238]
  294. [2, 3, 7, 78, 91]
  295. [2, 3, 8, 48, 48]
  296. [2, 3, 8, 36, 72]
  297. [2, 3, 8, 32, 96]
  298. [2, 3, 8, 30, 120]
  299. [2, 3, 8, 28, 168]
  300. [2, 3, 8, 27, 216]
  301. [2, 3, 8, 26, 312]
  302. [2, 3, 8, 25, 600]
  303. [2, 3, 8, 40, 60]
  304. [2, 3, 8, 42, 56]
  305. [2, 3, 8, 33, 88]
  306. [2, 3, 9, 36, 36]
  307. [2, 3, 9, 27, 54]
  308. [2, 3, 9, 24, 72]
  309. [2, 3, 9, 21, 126]
  310. [2, 3, 9, 20, 180]
  311. [2, 3, 9, 19, 342]
  312. [2, 3, 9, 30, 45]
  313. [2, 3, 9, 22, 99]
  314. [2, 3, 10, 30, 30]
  315. [2, 3, 10, 20, 60]
  316. [2, 3, 10, 18, 90]
  317. [2, 3, 10, 16, 240]
  318. [2, 3, 10, 24, 40]
  319. [2, 3, 11, 22, 33]
  320. [2, 3, 11, 14, 231]
  321. [2, 3, 11, 15, 110]
  322. [2, 3, 12, 24, 24]
  323. [2, 3, 12, 18, 36]
  324. [2, 3, 12, 16, 48]
  325. [2, 3, 12, 15, 60]
  326. [2, 3, 12, 14, 84]
  327. [2, 3, 12, 13, 156]
  328. [2, 3, 12, 20, 30]
  329. [2, 3, 12, 21, 28]
  330. [2, 3, 13, 13, 78]
  331. [2, 3, 14, 14, 42]
  332. [2, 3, 15, 15, 30]
  333. [2, 3, 16, 16, 24]
  334. [2, 3, 18, 18, 18]
  335. [2, 4, 5, 40, 40]
  336. [2, 4, 5, 30, 60]
  337. [2, 4, 5, 25, 100]
  338. [2, 4, 5, 24, 120]
  339. [2, 4, 5, 22, 220]
  340. [2, 4, 5, 21, 420]
  341. [2, 4, 5, 28, 70]
  342. [2, 4, 5, 36, 45]
  343. [2, 4, 6, 24, 24]
  344. [2, 4, 6, 18, 36]
  345. [2, 4, 6, 16, 48]
  346. [2, 4, 6, 15, 60]
  347. [2, 4, 6, 14, 84]
  348. [2, 4, 6, 13, 156]
  349. [2, 4, 6, 20, 30]
  350. [2, 4, 6, 21, 28]
  351. [2, 4, 7, 14, 28]
  352. [2, 4, 7, 10, 140]
  353. [2, 4, 7, 12, 42]
  354. [2, 4, 8, 16, 16]
  355. [2, 4, 8, 12, 24]
  356. [2, 4, 8, 10, 40]
  357. [2, 4, 8, 9, 72]
  358. [2, 4, 9, 9, 36]
  359. [2, 4, 9, 12, 18]
  360. [2, 4, 10, 10, 20]
  361. [2, 4, 10, 12, 15]
  362. [2, 4, 12, 12, 12]
  363. [2, 5, 5, 20, 20]
  364. [2, 5, 5, 15, 30]
  365. [2, 5, 5, 12, 60]
  366. [2, 5, 5, 11, 110]
  367. [2, 5, 5, 14, 35]
  368. [2, 5, 6, 10, 30]
  369. [2, 5, 6, 8, 120]
  370. [2, 5, 6, 12, 20]
  371. [2, 5, 7, 7, 70]
  372. [2, 5, 8, 8, 20]
  373. [2, 5, 10, 10, 10]
  374. [2, 6, 6, 12, 12]
  375. [2, 6, 6, 9, 18]
  376. [2, 6, 6, 8, 24]
  377. [2, 6, 6, 7, 42]
  378. [2, 6, 6, 10, 15]
  379. [2, 6, 8, 8, 12]
  380. [2, 7, 7, 7, 14]
  381. [2, 8, 8, 8, 8]
  382. [3, 3, 4, 24, 24]
  383. [3, 3, 4, 18, 36]
  384. [3, 3, 4, 16, 48]
  385. [3, 3, 4, 15, 60]
  386. [3, 3, 4, 14, 84]
  387. [3, 3, 4, 13, 156]
  388. [3, 3, 4, 20, 30]
  389. [3, 3, 4, 21, 28]
  390. [3, 3, 5, 15, 15]
  391. [3, 3, 5, 10, 30]
  392. [3, 3, 5, 9, 45]
  393. [3, 3, 5, 8, 120]
  394. [3, 3, 5, 12, 20]
  395. [3, 3, 6, 12, 12]
  396. [3, 3, 6, 9, 18]
  397. [3, 3, 6, 8, 24]
  398. [3, 3, 6, 7, 42]
  399. [3, 3, 6, 10, 15]
  400. [3, 3, 7, 7, 21]
  401. [3, 3, 8, 8, 12]
  402. [3, 3, 9, 9, 9]
  403. [3, 4, 4, 12, 12]
  404. [3, 4, 4, 8, 24]
  405. [3, 4, 5, 5, 60]
  406. [3, 4, 5, 6, 20]
  407. [3, 4, 6, 6, 12]
  408. [3, 5, 5, 5, 15]
  409. [3, 5, 5, 6, 10]
  410. [3, 6, 6, 6, 6]
  411. [4, 4, 4, 8, 8]
  412. [4, 4, 4, 6, 12]
  413. [4, 4, 4, 5, 20]
  414. [5, 5, 5, 5, 5]
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毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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medie2005
发表于 2010-1-19 09:20:13 | 显示全部楼层
7# mathe
漏了很多解，比如5个1/5。
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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mathe
发表于 2010-1-19 09:21:52 | 显示全部楼层
前面要求数据都不重复时N=7的结果也出来了,是190576个,结果文件总共6.1M.
而数据可以重复时,N=6有2996个
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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