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[分享] 倒数之和为1

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数论爱好者
发表于 2011-9-11 19:19:09 | 显示全部楼层 |阅读模式

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有6个不同的自然数，它们的倒数之和为1，求这6个自然数 $1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}=1$ 我是没有解出来，但现在我已经知道答案了 看看大家如何解，再公布答案
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 2011-9-11 19:28:40 | 显示全部楼层
数字最大（或字典序最小）的解： $1/2+1/3+1/7+1/43+1/1807+1/3263442=1$ 不知道数字最小的解是多少。
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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数论爱好者
 楼主| 发表于 2011-9-12 00:09:50 | 显示全部楼层
1/2+1/3+1/9+1/27+1/81+1/162=1 1/2=1/3+1/6 1=1/2+1/3+1/6 =1/2+1/3+(1/3)*(1/3+1/6) =1/2+1/3+1/9+(1/9)*(1/3+1/6) =…… =1/2+1/3+1/9+1/27+1/81+1/162
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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gxqcn
发表于 2011-9-12 21:38:36 | 显示全部楼层
调出我十多年前用VB开发的《埃及分数分解》程序，设定“禁止重复真分数”及分解分数分母上限=162，得到的结果如下：
  1. No.1 1 = 1/2 + 1/3 + 1/7 + 1/96 + 1/140 + 1/160
  2. No.2 1 = 1/2 + 1/3 + 1/7 + 1/100 + 1/140 + 1/150
  3. No.3 1 = 1/2 + 1/3 + 1/7 + 1/108 + 1/135 + 1/140
  4. No.4 1 = 1/2 + 1/3 + 1/7 + 1/110 + 1/132 + 1/140
  5. No.5 1 = 1/2 + 1/3 + 1/7 + 1/112 + 1/126 + 1/144
  6. No.6 1 = 1/2 + 1/3 + 1/8 + 1/36 + 1/136 + 1/153
  7. No.7 1 = 1/2 + 1/3 + 1/8 + 1/38 + 1/114 + 1/152
  8. No.8 1 = 1/2 + 1/3 + 1/8 + 1/39 + 1/104 + 1/156
  9. No.9 1 = 1/2 + 1/3 + 1/8 + 1/39 + 1/120 + 1/130
  10. No.10 1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/96 + 1/160
  11. No.11 1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/100 + 1/150
  12. No.12 1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/105 + 1/140
  13. No.13 1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/108 + 1/135
  14. No.14 1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/110 + 1/132
  15. No.15 1 = 1/2 + 1/3 + 1/8 + 1/42 + 1/88 + 1/154
  16. No.16 1 = 1/2 + 1/3 + 1/8 + 1/42 + 1/105 + 1/120
  17. No.17 1 = 1/2 + 1/3 + 1/8 + 1/44 + 1/88 + 1/132
  18. No.18 1 = 1/2 + 1/3 + 1/8 + 1/45 + 1/80 + 1/144
  19. No.19 1 = 1/2 + 1/3 + 1/8 + 1/45 + 1/90 + 1/120
  20. No.20 1 = 1/2 + 1/3 + 1/8 + 1/48 + 1/72 + 1/144
  21. No.21 1 = 1/2 + 1/3 + 1/8 + 1/48 + 1/80 + 1/120
  22. No.22 1 = 1/2 + 1/3 + 1/8 + 1/48 + 1/84 + 1/112
  23. No.23 1 = 1/2 + 1/3 + 1/8 + 1/50 + 1/75 + 1/120
  24. No.24 1 = 1/2 + 1/3 + 1/8 + 1/51 + 1/68 + 1/136
  25. No.25 1 = 1/2 + 1/3 + 1/8 + 1/52 + 1/72 + 1/117
  26. No.26 1 = 1/2 + 1/3 + 1/8 + 1/52 + 1/78 + 1/104
  27. No.27 1 = 1/2 + 1/3 + 1/8 + 1/54 + 1/72 + 1/108
  28. No.28 1 = 1/2 + 1/3 + 1/8 + 1/55 + 1/66 + 1/120
  29. No.29 1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/60 + 1/140
  30. No.30 1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/63 + 1/126
  31. No.31 1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/70 + 1/105
  32. No.32 1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/78 + 1/91
  33. No.33 1 = 1/2 + 1/3 + 1/8 + 1/60 + 1/65 + 1/104
  34. No.34 1 = 1/2 + 1/3 + 1/8 + 1/60 + 1/72 + 1/90
  35. No.35 1 = 1/2 + 1/3 + 1/8 + 1/63 + 1/72 + 1/84
  36. No.36 1 = 1/2 + 1/3 + 1/9 + 1/24 + 1/136 + 1/153
  37. No.37 1 = 1/2 + 1/3 + 1/9 + 1/26 + 1/99 + 1/143
  38. No.38 1 = 1/2 + 1/3 + 1/9 + 1/27 + 1/81 + 1/162
  39. No.39 1 = 1/2 + 1/3 + 1/9 + 1/27 + 1/90 + 1/135
  40. No.40 1 = 1/2 + 1/3 + 1/9 + 1/28 + 1/84 + 1/126
  41. No.41 1 = 1/2 + 1/3 + 1/9 + 1/30 + 1/70 + 1/126
  42. No.42 1 = 1/2 + 1/3 + 1/9 + 1/30 + 1/72 + 1/120
  43. No.43 1 = 1/2 + 1/3 + 1/9 + 1/32 + 1/72 + 1/96
  44. No.44 1 = 1/2 + 1/3 + 1/9 + 1/33 + 1/66 + 1/99
  45. No.45 1 = 1/2 + 1/3 + 1/9 + 1/33 + 1/72 + 1/88
  46. No.46 1 = 1/2 + 1/3 + 1/9 + 1/34 + 1/51 + 1/153
  47. No.47 1 = 1/2 + 1/3 + 1/9 + 1/35 + 1/63 + 1/90
  48. No.48 1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/48 + 1/144
  49. No.49 1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/52 + 1/117
  50. No.50 1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/54 + 1/108
  51. No.51 1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/60 + 1/90
  52. No.52 1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/63 + 1/84
  53. No.53 1 = 1/2 + 1/3 + 1/9 + 1/39 + 1/45 + 1/130
  54. No.54 1 = 1/2 + 1/3 + 1/9 + 1/40 + 1/45 + 1/120
  55. No.55 1 = 1/2 + 1/3 + 1/9 + 1/40 + 1/60 + 1/72
  56. No.56 1 = 1/2 + 1/3 + 1/9 + 1/42 + 1/45 + 1/105
  57. No.57 1 = 1/2 + 1/3 + 1/9 + 1/42 + 1/56 + 1/72
  58. No.58 1 = 1/2 + 1/3 + 1/9 + 1/45 + 1/48 + 1/80
  59. No.59 1 = 1/2 + 1/3 + 1/9 + 1/45 + 1/50 + 1/75
  60. No.60 1 = 1/2 + 1/3 + 1/9 + 1/45 + 1/55 + 1/66
  61. No.61 1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/96 + 1/160
  62. No.62 1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/100 + 1/150
  63. No.63 1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/105 + 1/140
  64. No.64 1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/108 + 1/135
  65. No.65 1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/110 + 1/132
  66. No.66 1 = 1/2 + 1/3 + 1/10 + 1/21 + 1/84 + 1/140
  67. No.67 1 = 1/2 + 1/3 + 1/10 + 1/21 + 1/90 + 1/126
  68. No.68 1 = 1/2 + 1/3 + 1/10 + 1/22 + 1/90 + 1/99
  69. No.69 1 = 1/2 + 1/3 + 1/10 + 1/23 + 1/69 + 1/115
  70. No.70 1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/56 + 1/140
  71. No.71 1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/60 + 1/120
  72. No.72 1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/65 + 1/104
  73. No.73 1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/72 + 1/90
  74. No.74 1 = 1/2 + 1/3 + 1/10 + 1/25 + 1/50 + 1/150
  75. No.75 1 = 1/2 + 1/3 + 1/10 + 1/25 + 1/60 + 1/100
  76. No.76 1 = 1/2 + 1/3 + 1/10 + 1/26 + 1/65 + 1/78
  77. No.77 1 = 1/2 + 1/3 + 1/10 + 1/27 + 1/45 + 1/135
  78. No.78 1 = 1/2 + 1/3 + 1/10 + 1/27 + 1/54 + 1/90
  79. No.79 1 = 1/2 + 1/3 + 1/10 + 1/28 + 1/42 + 1/140
  80. No.80 1 = 1/2 + 1/3 + 1/10 + 1/28 + 1/60 + 1/70
  81. No.81 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/39 + 1/130
  82. No.82 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/40 + 1/120
  83. No.83 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/42 + 1/105
  84. No.84 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/45 + 1/90
  85. No.85 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/48 + 1/80
  86. No.86 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/50 + 1/75
  87. No.87 1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/55 + 1/66
  88. No.88 1 = 1/2 + 1/3 + 1/10 + 1/32 + 1/40 + 1/96
  89. No.89 1 = 1/2 + 1/3 + 1/10 + 1/33 + 1/40 + 1/88
  90. No.90 1 = 1/2 + 1/3 + 1/10 + 1/35 + 1/42 + 1/70
  91. No.91 1 = 1/2 + 1/3 + 1/10 + 1/35 + 1/45 + 1/63
  92. No.92 1 = 1/2 + 1/3 + 1/10 + 1/36 + 1/40 + 1/72
  93. No.93 1 = 1/2 + 1/3 + 1/10 + 1/36 + 1/45 + 1/60
  94. No.94 1 = 1/2 + 1/3 + 1/10 + 1/40 + 1/42 + 1/56
  95. No.95 1 = 1/2 + 1/3 + 1/11 + 1/18 + 1/90 + 1/110
  96. No.96 1 = 1/2 + 1/3 + 1/11 + 1/20 + 1/55 + 1/132
  97. No.97 1 = 1/2 + 1/3 + 1/11 + 1/20 + 1/60 + 1/110
  98. No.98 1 = 1/2 + 1/3 + 1/11 + 1/21 + 1/66 + 1/77
  99. No.99 1 = 1/2 + 1/3 + 1/11 + 1/22 + 1/42 + 1/154
  100. No.100 1 = 1/2 + 1/3 + 1/11 + 1/22 + 1/44 + 1/132
  101. No.101 1 = 1/2 + 1/3 + 1/11 + 1/24 + 1/40 + 1/110
  102. No.102 1 = 1/2 + 1/3 + 1/11 + 1/24 + 1/44 + 1/88
  103. No.103 1 = 1/2 + 1/3 + 1/11 + 1/26 + 1/33 + 1/143
  104. No.104 1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/96 + 1/160
  105. No.105 1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/100 + 1/150
  106. No.106 1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/105 + 1/140
  107. No.107 1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/108 + 1/135
  108. No.108 1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/110 + 1/132
  109. No.109 1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/72 + 1/144
  110. No.110 1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/80 + 1/120
  111. No.111 1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/84 + 1/112
  112. No.112 1 = 1/2 + 1/3 + 1/12 + 1/17 + 1/68 + 1/102
  113. No.113 1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/48 + 1/144
  114. No.114 1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/52 + 1/117
  115. No.115 1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/54 + 1/108
  116. No.116 1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/60 + 1/90
  117. No.117 1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/63 + 1/84
  118. No.118 1 = 1/2 + 1/3 + 1/12 + 1/19 + 1/57 + 1/76
  119. No.119 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/39 + 1/130
  120. No.120 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/40 + 1/120
  121. No.121 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/42 + 1/105
  122. No.122 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/45 + 1/90
  123. No.123 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/48 + 1/80
  124. No.124 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/50 + 1/75
  125. No.125 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/55 + 1/66
  126. No.126 1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/35 + 1/140
  127. No.127 1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/36 + 1/126
  128. No.128 1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/42 + 1/84
  129. No.129 1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/44 + 1/77
  130. No.130 1 = 1/2 + 1/3 + 1/12 + 1/22 + 1/33 + 1/132
  131. No.131 1 = 1/2 + 1/3 + 1/12 + 1/22 + 1/36 + 1/99
  132. No.132 1 = 1/2 + 1/3 + 1/12 + 1/22 + 1/44 + 1/66
  133. No.133 1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/30 + 1/120
  134. No.134 1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/32 + 1/96
  135. No.135 1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/33 + 1/88
  136. No.136 1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/36 + 1/72
  137. No.137 1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/40 + 1/60
  138. No.138 1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/42 + 1/56
  139. No.139 1 = 1/2 + 1/3 + 1/12 + 1/25 + 1/30 + 1/100
  140. No.140 1 = 1/2 + 1/3 + 1/12 + 1/26 + 1/39 + 1/52
  141. No.141 1 = 1/2 + 1/3 + 1/12 + 1/27 + 1/36 + 1/54
  142. No.142 1 = 1/2 + 1/3 + 1/12 + 1/28 + 1/30 + 1/70
  143. No.143 1 = 1/2 + 1/3 + 1/12 + 1/30 + 1/36 + 1/45
  144. No.144 1 = 1/2 + 1/3 + 1/13 + 1/14 + 1/84 + 1/156
  145. No.145 1 = 1/2 + 1/3 + 1/13 + 1/15 + 1/60 + 1/156
  146. No.146 1 = 1/2 + 1/3 + 1/13 + 1/15 + 1/65 + 1/130
  147. No.147 1 = 1/2 + 1/3 + 1/13 + 1/16 + 1/48 + 1/156
  148. No.148 1 = 1/2 + 1/3 + 1/13 + 1/18 + 1/36 + 1/156
  149. No.149 1 = 1/2 + 1/3 + 1/13 + 1/18 + 1/39 + 1/117
  150. No.150 1 = 1/2 + 1/3 + 1/13 + 1/20 + 1/30 + 1/156
  151. No.151 1 = 1/2 + 1/3 + 1/13 + 1/21 + 1/28 + 1/156
  152. No.152 1 = 1/2 + 1/3 + 1/13 + 1/24 + 1/26 + 1/104
  153. No.153 1 = 1/2 + 1/3 + 1/14 + 1/15 + 1/60 + 1/84
  154. No.154 1 = 1/2 + 1/3 + 1/14 + 1/16 + 1/42 + 1/112
  155. No.155 1 = 1/2 + 1/3 + 1/14 + 1/16 + 1/48 + 1/84
  156. No.156 1 = 1/2 + 1/3 + 1/14 + 1/18 + 1/35 + 1/90
  157. No.157 1 = 1/2 + 1/3 + 1/14 + 1/18 + 1/36 + 1/84
  158. No.158 1 = 1/2 + 1/3 + 1/14 + 1/18 + 1/42 + 1/63
  159. No.159 1 = 1/2 + 1/3 + 1/14 + 1/20 + 1/28 + 1/105
  160. No.160 1 = 1/2 + 1/3 + 1/14 + 1/20 + 1/30 + 1/84
  161. No.161 1 = 1/2 + 1/3 + 1/14 + 1/20 + 1/35 + 1/60
  162. No.162 1 = 1/2 + 1/3 + 1/14 + 1/21 + 1/28 + 1/84
  163. No.163 1 = 1/2 + 1/3 + 1/14 + 1/21 + 1/30 + 1/70
  164. No.164 1 = 1/2 + 1/3 + 1/14 + 1/24 + 1/28 + 1/56
  165. No.165 1 = 1/2 + 1/3 + 1/14 + 1/24 + 1/35 + 1/40
  166. No.166 1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/32 + 1/160
  167. No.167 1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/35 + 1/112
  168. No.168 1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/40 + 1/80
  169. No.169 1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/48 + 1/60
  170. No.170 1 = 1/2 + 1/3 + 1/15 + 1/17 + 1/34 + 1/85
  171. No.171 1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/27 + 1/135
  172. No.172 1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/30 + 1/90
  173. No.173 1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/35 + 1/63
  174. No.174 1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/36 + 1/60
  175. No.175 1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/24 + 1/120
  176. No.176 1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/25 + 1/100
  177. No.177 1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/28 + 1/70
  178. No.178 1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/30 + 1/60
  179. No.179 1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/36 + 1/45
  180. No.180 1 = 1/2 + 1/3 + 1/15 + 1/21 + 1/28 + 1/60
  181. No.181 1 = 1/2 + 1/3 + 1/15 + 1/21 + 1/35 + 1/42
  182. No.182 1 = 1/2 + 1/3 + 1/15 + 1/24 + 1/30 + 1/40
  183. No.183 1 = 1/2 + 1/3 + 1/16 + 1/18 + 1/24 + 1/144
  184. No.184 1 = 1/2 + 1/3 + 1/16 + 1/18 + 1/36 + 1/48
  185. No.185 1 = 1/2 + 1/3 + 1/16 + 1/20 + 1/24 + 1/80
  186. No.186 1 = 1/2 + 1/3 + 1/16 + 1/20 + 1/30 + 1/48
  187. No.187 1 = 1/2 + 1/3 + 1/16 + 1/21 + 1/28 + 1/48
  188. No.188 1 = 1/2 + 1/3 + 1/18 + 1/20 + 1/30 + 1/36
  189. No.189 1 = 1/2 + 1/3 + 1/18 + 1/21 + 1/28 + 1/36
  190. No.190 1 = 1/2 + 1/3 + 1/20 + 1/21 + 1/28 + 1/30
  191. No.191 1 = 1/2 + 1/4 + 1/5 + 1/29 + 1/116 + 1/145
  192. No.192 1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/96 + 1/160
  193. No.193 1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/100 + 1/150
  194. No.194 1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/105 + 1/140
  195. No.195 1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/108 + 1/135
  196. No.196 1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/110 + 1/132
  197. No.197 1 = 1/2 + 1/4 + 1/5 + 1/32 + 1/80 + 1/160
  198. No.198 1 = 1/2 + 1/4 + 1/5 + 1/32 + 1/96 + 1/120
  199. No.199 1 = 1/2 + 1/4 + 1/5 + 1/33 + 1/88 + 1/120
  200. No.200 1 = 1/2 + 1/4 + 1/5 + 1/35 + 1/70 + 1/140
  201. No.201 1 = 1/2 + 1/4 + 1/5 + 1/35 + 1/80 + 1/112
  202. No.202 1 = 1/2 + 1/4 + 1/5 + 1/35 + 1/84 + 1/105
  203. No.203 1 = 1/2 + 1/4 + 1/5 + 1/36 + 1/70 + 1/126
  204. No.204 1 = 1/2 + 1/4 + 1/5 + 1/36 + 1/72 + 1/120
  205. No.205 1 = 1/2 + 1/4 + 1/5 + 1/38 + 1/76 + 1/95
  206. No.206 1 = 1/2 + 1/4 + 1/5 + 1/39 + 1/60 + 1/130
  207. No.207 1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/56 + 1/140
  208. No.208 1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/60 + 1/120
  209. No.209 1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/65 + 1/104
  210. No.210 1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/72 + 1/90
  211. No.211 1 = 1/2 + 1/4 + 1/5 + 1/42 + 1/56 + 1/120
  212. No.212 1 = 1/2 + 1/4 + 1/5 + 1/42 + 1/60 + 1/105
  213. No.213 1 = 1/2 + 1/4 + 1/5 + 1/42 + 1/70 + 1/84
  214. No.214 1 = 1/2 + 1/4 + 1/5 + 1/44 + 1/55 + 1/110
  215. No.215 1 = 1/2 + 1/4 + 1/5 + 1/44 + 1/70 + 1/77
  216. No.216 1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/48 + 1/144
  217. No.217 1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/52 + 1/117
  218. No.218 1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/54 + 1/108
  219. No.219 1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/60 + 1/90
  220. No.220 1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/63 + 1/84
  221. No.221 1 = 1/2 + 1/4 + 1/5 + 1/48 + 1/60 + 1/80
  222. No.222 1 = 1/2 + 1/4 + 1/5 + 1/50 + 1/60 + 1/75
  223. No.223 1 = 1/2 + 1/4 + 1/5 + 1/55 + 1/60 + 1/66
  224. No.224 1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/96 + 1/160
  225. No.225 1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/100 + 1/150
  226. No.226 1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/105 + 1/140
  227. No.227 1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/108 + 1/135
  228. No.228 1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/110 + 1/132
  229. No.229 1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/72 + 1/144
  230. No.230 1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/80 + 1/120
  231. No.231 1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/84 + 1/112
  232. No.232 1 = 1/2 + 1/4 + 1/6 + 1/17 + 1/68 + 1/102
  233. No.233 1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/48 + 1/144
  234. No.234 1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/52 + 1/117
  235. No.235 1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/54 + 1/108
  236. No.236 1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/60 + 1/90
  237. No.237 1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/63 + 1/84
  238. No.238 1 = 1/2 + 1/4 + 1/6 + 1/19 + 1/57 + 1/76
  239. No.239 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/39 + 1/130
  240. No.240 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/40 + 1/120
  241. No.241 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/42 + 1/105
  242. No.242 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/45 + 1/90
  243. No.243 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/48 + 1/80
  244. No.244 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/50 + 1/75
  245. No.245 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/55 + 1/66
  246. No.246 1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/35 + 1/140
  247. No.247 1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/36 + 1/126
  248. No.248 1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/42 + 1/84
  249. No.249 1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/44 + 1/77
  250. No.250 1 = 1/2 + 1/4 + 1/6 + 1/22 + 1/33 + 1/132
  251. No.251 1 = 1/2 + 1/4 + 1/6 + 1/22 + 1/36 + 1/99
  252. No.252 1 = 1/2 + 1/4 + 1/6 + 1/22 + 1/44 + 1/66
  253. No.253 1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/30 + 1/120
  254. No.254 1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/32 + 1/96
  255. No.255 1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/33 + 1/88
  256. No.256 1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/36 + 1/72
  257. No.257 1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/40 + 1/60
  258. No.258 1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/42 + 1/56
  259. No.259 1 = 1/2 + 1/4 + 1/6 + 1/25 + 1/30 + 1/100
  260. No.260 1 = 1/2 + 1/4 + 1/6 + 1/26 + 1/39 + 1/52
  261. No.261 1 = 1/2 + 1/4 + 1/6 + 1/27 + 1/36 + 1/54
  262. No.262 1 = 1/2 + 1/4 + 1/6 + 1/28 + 1/30 + 1/70
  263. No.263 1 = 1/2 + 1/4 + 1/6 + 1/30 + 1/36 + 1/45
  264. No.264 1 = 1/2 + 1/4 + 1/7 + 1/11 + 1/110 + 1/140
  265. No.265 1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/60 + 1/140
  266. No.266 1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/63 + 1/126
  267. No.267 1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/70 + 1/105
  268. No.268 1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/78 + 1/91
  269. No.269 1 = 1/2 + 1/4 + 1/7 + 1/13 + 1/42 + 1/156
  270. No.270 1 = 1/2 + 1/4 + 1/7 + 1/13 + 1/52 + 1/91
  271. No.271 1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/35 + 1/140
  272. No.272 1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/36 + 1/126
  273. No.273 1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/42 + 1/84
  274. No.274 1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/44 + 1/77
  275. No.275 1 = 1/2 + 1/4 + 1/7 + 1/15 + 1/30 + 1/140
  276. No.276 1 = 1/2 + 1/4 + 1/7 + 1/15 + 1/35 + 1/84
  277. No.277 1 = 1/2 + 1/4 + 1/7 + 1/15 + 1/42 + 1/60
  278. No.278 1 = 1/2 + 1/4 + 1/7 + 1/16 + 1/28 + 1/112
  279. No.279 1 = 1/2 + 1/4 + 1/7 + 1/16 + 1/42 + 1/48
  280. No.280 1 = 1/2 + 1/4 + 1/7 + 1/18 + 1/28 + 1/63
  281. No.281 1 = 1/2 + 1/4 + 1/7 + 1/18 + 1/36 + 1/42
  282. No.282 1 = 1/2 + 1/4 + 1/7 + 1/20 + 1/21 + 1/105
  283. No.283 1 = 1/2 + 1/4 + 1/7 + 1/20 + 1/30 + 1/42
  284. No.284 1 = 1/2 + 1/4 + 1/7 + 1/21 + 1/24 + 1/56
  285. No.285 1 = 1/2 + 1/4 + 1/7 + 1/21 + 1/28 + 1/42
  286. No.286 1 = 1/2 + 1/4 + 1/8 + 1/9 + 1/136 + 1/153
  287. No.287 1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/56 + 1/140
  288. No.288 1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/60 + 1/120
  289. No.289 1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/65 + 1/104
  290. No.290 1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/72 + 1/90
  291. No.291 1 = 1/2 + 1/4 + 1/8 + 1/11 + 1/40 + 1/110
  292. No.292 1 = 1/2 + 1/4 + 1/8 + 1/11 + 1/44 + 1/88
  293. No.293 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/30 + 1/120
  294. No.294 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/32 + 1/96
  295. No.295 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/33 + 1/88
  296. No.296 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/36 + 1/72
  297. No.297 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/40 + 1/60
  298. No.298 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/42 + 1/56
  299. No.299 1 = 1/2 + 1/4 + 1/8 + 1/13 + 1/24 + 1/156
  300. No.300 1 = 1/2 + 1/4 + 1/8 + 1/13 + 1/26 + 1/104
  301. No.301 1 = 1/2 + 1/4 + 1/8 + 1/14 + 1/24 + 1/84
  302. No.302 1 = 1/2 + 1/4 + 1/8 + 1/14 + 1/28 + 1/56
  303. No.303 1 = 1/2 + 1/4 + 1/8 + 1/14 + 1/35 + 1/40
  304. No.304 1 = 1/2 + 1/4 + 1/8 + 1/15 + 1/20 + 1/120
  305. No.305 1 = 1/2 + 1/4 + 1/8 + 1/15 + 1/24 + 1/60
  306. No.306 1 = 1/2 + 1/4 + 1/8 + 1/15 + 1/30 + 1/40
  307. No.307 1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/18 + 1/144
  308. No.308 1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/20 + 1/80
  309. No.309 1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/24 + 1/48
  310. No.310 1 = 1/2 + 1/4 + 1/8 + 1/18 + 1/24 + 1/36
  311. No.311 1 = 1/2 + 1/4 + 1/8 + 1/20 + 1/24 + 1/30
  312. No.312 1 = 1/2 + 1/4 + 1/8 + 1/21 + 1/24 + 1/28
  313. No.313 1 = 1/2 + 1/4 + 1/9 + 1/10 + 1/36 + 1/90
  314. No.314 1 = 1/2 + 1/4 + 1/9 + 1/10 + 1/40 + 1/72
  315. No.315 1 = 1/2 + 1/4 + 1/9 + 1/10 + 1/45 + 1/60
  316. No.316 1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/21 + 1/126
  317. No.317 1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/22 + 1/99
  318. No.318 1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/24 + 1/72
  319. No.319 1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/27 + 1/54
  320. No.320 1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/30 + 1/45
  321. No.321 1 = 1/2 + 1/4 + 1/9 + 1/13 + 1/18 + 1/156
  322. No.322 1 = 1/2 + 1/4 + 1/9 + 1/14 + 1/18 + 1/84
  323. No.323 1 = 1/2 + 1/4 + 1/9 + 1/15 + 1/18 + 1/60
  324. No.324 1 = 1/2 + 1/4 + 1/9 + 1/15 + 1/20 + 1/45
  325. No.325 1 = 1/2 + 1/4 + 1/9 + 1/16 + 1/18 + 1/48
  326. No.326 1 = 1/2 + 1/4 + 1/9 + 1/18 + 1/20 + 1/30
  327. No.327 1 = 1/2 + 1/4 + 1/9 + 1/18 + 1/21 + 1/28
  328. No.328 1 = 1/2 + 1/4 + 1/10 + 1/11 + 1/20 + 1/110
  329. No.329 1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/18 + 1/90
  330. No.330 1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/20 + 1/60
  331. No.331 1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/24 + 1/40
  332. No.332 1 = 1/2 + 1/4 + 1/10 + 1/13 + 1/15 + 1/156
  333. No.333 1 = 1/2 + 1/4 + 1/10 + 1/14 + 1/15 + 1/84
  334. No.334 1 = 1/2 + 1/4 + 1/10 + 1/14 + 1/20 + 1/35
  335. No.335 1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/16 + 1/48
  336. No.336 1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/18 + 1/36
  337. No.337 1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/20 + 1/30
  338. No.338 1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/21 + 1/28
  339. No.339 1 = 1/2 + 1/4 + 1/11 + 1/12 + 1/15 + 1/110
  340. No.340 1 = 1/2 + 1/4 + 1/11 + 1/12 + 1/22 + 1/33
  341. No.341 1 = 1/2 + 1/4 + 1/12 + 1/14 + 1/15 + 1/35
  342. No.342 1 = 1/2 + 1/5 + 1/6 + 1/9 + 1/70 + 1/126
  343. No.343 1 = 1/2 + 1/5 + 1/6 + 1/9 + 1/72 + 1/120
  344. No.344 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/39 + 1/130
  345. No.345 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/40 + 1/120
  346. No.346 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/42 + 1/105
  347. No.347 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/45 + 1/90
  348. No.348 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/48 + 1/80
  349. No.349 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/50 + 1/75
  350. No.350 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/55 + 1/66
  351. No.351 1 = 1/2 + 1/5 + 1/6 + 1/11 + 1/30 + 1/110
  352. No.352 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/24 + 1/120
  353. No.353 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/25 + 1/100
  354. No.354 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/28 + 1/70
  355. No.355 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/30 + 1/60
  356. No.356 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/36 + 1/45
  357. No.357 1 = 1/2 + 1/5 + 1/6 + 1/13 + 1/20 + 1/156
  358. No.358 1 = 1/2 + 1/5 + 1/6 + 1/14 + 1/20 + 1/84
  359. No.359 1 = 1/2 + 1/5 + 1/6 + 1/14 + 1/21 + 1/70
  360. No.360 1 = 1/2 + 1/5 + 1/6 + 1/14 + 1/30 + 1/35
  361. No.361 1 = 1/2 + 1/5 + 1/6 + 1/15 + 1/18 + 1/90
  362. No.362 1 = 1/2 + 1/5 + 1/6 + 1/15 + 1/20 + 1/60
  363. No.363 1 = 1/2 + 1/5 + 1/6 + 1/15 + 1/24 + 1/40
  364. No.364 1 = 1/2 + 1/5 + 1/6 + 1/16 + 1/20 + 1/48
  365. No.365 1 = 1/2 + 1/5 + 1/6 + 1/18 + 1/20 + 1/36
  366. No.366 1 = 1/2 + 1/5 + 1/6 + 1/20 + 1/21 + 1/28
  367. No.367 1 = 1/2 + 1/5 + 1/7 + 1/8 + 1/40 + 1/140
  368. No.368 1 = 1/2 + 1/5 + 1/7 + 1/8 + 1/42 + 1/120
  369. No.369 1 = 1/2 + 1/5 + 1/7 + 1/8 + 1/56 + 1/70
  370. No.370 1 = 1/2 + 1/5 + 1/7 + 1/9 + 1/42 + 1/45
  371. No.371 1 = 1/2 + 1/5 + 1/7 + 1/10 + 1/20 + 1/140
  372. No.372 1 = 1/2 + 1/5 + 1/7 + 1/10 + 1/21 + 1/105
  373. No.373 1 = 1/2 + 1/5 + 1/7 + 1/10 + 1/30 + 1/42
  374. No.374 1 = 1/2 + 1/5 + 1/7 + 1/12 + 1/15 + 1/140
  375. No.375 1 = 1/2 + 1/5 + 1/7 + 1/12 + 1/20 + 1/42
  376. No.376 1 = 1/2 + 1/5 + 1/7 + 1/14 + 1/20 + 1/28
  377. No.377 1 = 1/2 + 1/5 + 1/8 + 1/9 + 1/18 + 1/120
  378. No.378 1 = 1/2 + 1/5 + 1/8 + 1/9 + 1/20 + 1/72
  379. No.379 1 = 1/2 + 1/5 + 1/8 + 1/9 + 1/24 + 1/45
  380. No.380 1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/15 + 1/120
  381. No.381 1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/16 + 1/80
  382. No.382 1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/20 + 1/40
  383. No.383 1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/24 + 1/30
  384. No.384 1 = 1/2 + 1/5 + 1/8 + 1/12 + 1/15 + 1/40
  385. No.385 1 = 1/2 + 1/5 + 1/8 + 1/12 + 1/20 + 1/24
  386. No.386 1 = 1/2 + 1/5 + 1/9 + 1/10 + 1/15 + 1/45
  387. No.387 1 = 1/2 + 1/5 + 1/9 + 1/10 + 1/18 + 1/30
  388. No.388 1 = 1/2 + 1/5 + 1/9 + 1/12 + 1/18 + 1/20
  389. No.389 1 = 1/2 + 1/5 + 1/10 + 1/12 + 1/15 + 1/20
  390. No.390 1 = 1/2 + 1/6 + 1/7 + 1/8 + 1/21 + 1/56
  391. No.391 1 = 1/2 + 1/6 + 1/7 + 1/8 + 1/24 + 1/42
  392. No.392 1 = 1/2 + 1/6 + 1/7 + 1/9 + 1/14 + 1/126
  393. No.393 1 = 1/2 + 1/6 + 1/7 + 1/9 + 1/18 + 1/42
  394. No.394 1 = 1/2 + 1/6 + 1/7 + 1/10 + 1/12 + 1/140
  395. No.395 1 = 1/2 + 1/6 + 1/7 + 1/10 + 1/15 + 1/42
  396. No.396 1 = 1/2 + 1/6 + 1/7 + 1/12 + 1/14 + 1/28
  397. No.397 1 = 1/2 + 1/6 + 1/8 + 1/9 + 1/12 + 1/72
  398. No.398 1 = 1/2 + 1/6 + 1/8 + 1/9 + 1/18 + 1/24
  399. No.399 1 = 1/2 + 1/6 + 1/8 + 1/10 + 1/12 + 1/40
  400. No.400 1 = 1/2 + 1/6 + 1/8 + 1/10 + 1/15 + 1/24
  401. No.401 1 = 1/2 + 1/6 + 1/9 + 1/10 + 1/15 + 1/18
  402. No.402 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/24 + 1/120
  403. No.403 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/25 + 1/100
  404. No.404 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/28 + 1/70
  405. No.405 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/30 + 1/60
  406. No.406 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/36 + 1/45
  407. No.407 1 = 1/3 + 1/4 + 1/5 + 1/7 + 1/15 + 1/140
  408. No.408 1 = 1/3 + 1/4 + 1/5 + 1/7 + 1/20 + 1/42
  409. No.409 1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/12 + 1/120
  410. No.410 1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/15 + 1/40
  411. No.411 1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/20 + 1/24
  412. No.412 1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/12 + 1/45
  413. No.413 1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/18 + 1/20
  414. No.414 1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30
  415. No.415 1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/15 + 1/20
  416. No.416 1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/10 + 1/140
  417. No.417 1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/12 + 1/42
  418. No.418 1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/14 + 1/28
  419. No.419 1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/9 + 1/72
  420. No.420 1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/10 + 1/40
  421. No.421 1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
  422. No.422 1 = 1/3 + 1/4 + 1/6 + 1/9 + 1/12 + 1/18
  423. No.423 1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15
复制代码
这是按字典排序输出的结果。
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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gxqcn
发表于 2011-9-12 21:39:48 | 显示全部楼层
数字最大（或字典序最小）的解： $1/2+1/3+1/7+1/43+1/1807+1/3263442=1$ 不知道数字最小的解是多少。 KeyTo9_Fans 发表于 2011-9-11 19:28
运行我的程序，结果确实如此。
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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geslon
发表于 2011-9-14 23:55:13 | 显示全部楼层
1分钟之内可以迅速找到一组解： 由于有 1=1/2+1/3+1/6 ------------------------------------(1) 的特性，又由于： 1=1/2+1/4+1/8+1/8 --------------------------------------(2) 将(1)两端乘以1/8,代入(2)式，就有： 1=1/2+1/4+1/8+1/16+1/24+1/48
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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wayne
发表于 2011-9-15 08:30:18 | 显示全部楼层
http://mathworld.wolfram.com/ZnamsProblem.html
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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