分类要考虑模式叠加 现在我实现了计数的程序了，运行结果如下:
Total 0 solution for 1 numbers
Total 0 solution for 2 numbers
Total 1 solution for 3 numbers
Total 6 solution for 4 numbers
Total 61 solution for 5 numbers
Total 635 solution for 6 numbers
Total 5562 solution for 7 numbers
Total 46530 solution for 8 numbers
Total 363835 solution for 9 numbers
Total 2677596 solution for 10 numbers
Total 18599967 solution for 11 numbers
Total 122231891 solution for 12 numbers
Total 761885131 solution for 13 numbers
Total 4519425241 solution for 14 numbers
Total 25587199368 solution for 15 numbers
Total 138556840936 solution for 16 numbers
real 2m36.923s
user 2m36.700s
sys 0m0.250s
也就是16个不同的埃及分数和为1的数目为138G.这个部分花费了157秒。
这个计算结果同liangbc的结果不同，我估计他的计算包含了相同的埃及分数的结果了。
不然两个不同埃及分数的和为1显然不可能，数目应该为0。
liangbc可以把你的代码修改一下，比较一下结果看看是否匹配。
不过这个程序运行速度看来没有想象的快。 Show下
看还有改进么 原帖由 mathe 于 2008-3-11 09:33 发表 http://bbs.emath.ac.cn/images/common/back.gif
现在我实现了计数的程序了，运行结果如下:
Total 0 solution for 1 numbers
Total 0 solution for 2 numbers
Total 1 solution for 3 numbers
Total 6 solution for 4 numbers
Total 61 solution for 5 numbers ... 感觉上面的结果有遗漏，我用2001年VB编的程序运行的结果如下：Total 0 solution for 1 numbers
Total 0 solution for 2 numbers
Total 1 solution for 3 numbers
Total 6 solution for 4 numbers
Total 62 solution for 5 numbers
Total 640 solution for 6 numbers
其中5个数的情形如下：No.1 1 = 1/2 + 1/3 + 1/7 + 1/51 + 1/238
No.2 1 = 1/2 + 1/3 + 1/7 + 1/54 + 1/189
No.3 1 = 1/2 + 1/3 + 1/7 + 1/56 + 1/168
No.4 1 = 1/2 + 1/3 + 1/7 + 1/60 + 1/140
No.5 1 = 1/2 + 1/3 + 1/7 + 1/63 + 1/126
No.6 1 = 1/2 + 1/3 + 1/7 + 1/70 + 1/105
No.7 1 = 1/2 + 1/3 + 1/7 + 1/78 + 1/91
No.8 1 = 1/2 + 1/3 + 1/8 + 1/27 + 1/216
No.9 1 = 1/2 + 1/3 + 1/8 + 1/28 + 1/168
No.10 1 = 1/2 + 1/3 + 1/8 + 1/30 + 1/120
No.11 1 = 1/2 + 1/3 + 1/8 + 1/32 + 1/96
No.12 1 = 1/2 + 1/3 + 1/8 + 1/33 + 1/88
No.13 1 = 1/2 + 1/3 + 1/8 + 1/36 + 1/72
No.14 1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/60
No.15 1 = 1/2 + 1/3 + 1/8 + 1/42 + 1/56
No.16 1 = 1/2 + 1/3 + 1/9 + 1/20 + 1/180
No.17 1 = 1/2 + 1/3 + 1/9 + 1/21 + 1/126
No.18 1 = 1/2 + 1/3 + 1/9 + 1/22 + 1/99
No.19 1 = 1/2 + 1/3 + 1/9 + 1/24 + 1/72
No.20 1 = 1/2 + 1/3 + 1/9 + 1/27 + 1/54
No.21 1 = 1/2 + 1/3 + 1/9 + 1/30 + 1/45
No.22 1 = 1/2 + 1/3 + 1/10 + 1/16 + 1/240
No.23 1 = 1/2 + 1/3 + 1/10 + 1/18 + 1/90
No.24 1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/60
No.25 1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/40
No.26 1 = 1/2 + 1/3 + 1/11 + 1/14 + 1/231
No.27 1 = 1/2 + 1/3 + 1/11 + 1/15 + 1/110
No.28 1 = 1/2 + 1/3 + 1/11 + 1/22 + 1/33
No.29 1 = 1/2 + 1/3 + 1/12 + 1/13 + 1/156
No.30 1 = 1/2 + 1/3 + 1/12 + 1/14 + 1/84
No.31 1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/60
No.32 1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/48
No.33 1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/36
No.34 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/30
No.35 1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/28
No.36 1 = 1/2 + 1/3 + 1/14 + 1/15 + 1/35
No.37 1 = 1/2 + 1/4 + 1/5 + 1/22 + 1/220
No.38 1 = 1/2 + 1/4 + 1/5 + 1/24 + 1/120
No.39 1 = 1/2 + 1/4 + 1/5 + 1/25 + 1/100
No.40 1 = 1/2 + 1/4 + 1/5 + 1/28 + 1/70
No.41 1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/60
No.42 1 = 1/2 + 1/4 + 1/5 + 1/36 + 1/45
No.43 1 = 1/2 + 1/4 + 1/6 + 1/13 + 1/156
No.44 1 = 1/2 + 1/4 + 1/6 + 1/14 + 1/84
No.45 1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/60
No.46 1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/48
No.47 1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/36
No.48 1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/30
No.49 1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/28
No.50 1 = 1/2 + 1/4 + 1/7 + 1/10 + 1/140
No.51 1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/42
No.52 1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/28
No.53 1 = 1/2 + 1/4 + 1/8 + 1/9 + 1/72
No.54 1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/40
No.55 1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/24
No.56 1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/18
No.57 1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/15
No.58 1 = 1/2 + 1/5 + 1/6 + 1/8 + 1/120
No.59 1 = 1/2 + 1/5 + 1/6 + 1/9 + 1/45
No.60 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/30
No.61 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/20
No.62 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20请查看是漏了哪组？
我上面的结果可能也有遗漏
因为程序设计中用的是全整型变量，当可能超出范围时，程序会给出“超标”指示，而实际上在运行过程中确实有该警示，
但比较肯定的是：搜索的结果应只多不少。
这是我的程序运行的结果，FYI
埃及分数分解：1（禁止重复 | 全奇数）No.1 1 = 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/15 + 1/21 + 1/135 + 1/10395
No.2 1 = 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/15 + 1/21 + 1/165 + 1/693
No.3 1 = 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/15 + 1/21 + 1/231 + 1/315
No.4 1 = 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/15 + 1/33 + 1/45 + 1/385
No.5 1 = 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/15 + 1/35 + 1/45 + 1/231设定分解项数≤10，但输出结果的项数却均=9
问题：将“1”分解成不重复的、且全奇数的埃及分数，是否有且仅有上述5组？ 终于找到BUG了，筛选27对应的模板时弄错了，使用的倍数280被误写成140了，结果错误了。
现在修改过来，附件里面有两个c文件，flter.c用于计数,fltere.c用于输出所有结果
比如现在flter.c在我的Linux上面运行243秒算出20以内的计数为:
Total 0 solution for 1 numbers
Total 0 solution for 2 numbers
Total 1 solution for 3 numbers
Total 6 solution for 4 numbers
Total 62 solution for 5 numbers
Total 642 solution for 6 numbers
Total 5623 solution for 7 numbers
Total 47126 solution for 8 numbers
Total 368680 solution for 9 numbers
Total 2715613 solution for 10 numbers
Total 18876751 solution for 11 numbers
Total 124137535 solution for 12 numbers
Total 774232619 solution for 13 numbers
Total 4595291801 solution for 14 numbers
Total 26030660449 solution for 15 numbers
Total 141031079451 solution for 16 numbers
Total 731862267491 solution for 17 numbers
Total 3641135367129 solution for 18 numbers
Total 17379359388167 solution for 19 numbers
Total 79633646141291 solution for 20 numbers
real 4m3.688s
user 4m3.330s
sys 0m0.310s
试着运行了fltere.c程序，输出所有10个数的情况
花费了10分半钟，产生一个136M的文本文件 Level 5我计算出来结果也是62，gxqcn上面那个结果是正确的 呵呵，现在提一个问题，不限制埃及分数的数目，那么使用分母在2到256之间的不同埃及分数构成1，总共有多少种方案。
估计一下计算机大概要花多长时间可以解出。