勾股判断题

ysr · 发表于 2021-2-15 19:54

验证大整数163500169的程序正在运行，都一个半小时了，还没有出来结果，这才是9位的整数，速度太慢，计算量太大。

ysr · 发表于 2021-2-15 21:39

本帖最后由 ysr 于 2021-2-15 13:40 编辑

少4组：（101~140之间应该19组而不是15组）少了第7组 0/解/20/99/101，第14组解： 0/解/15/112/113，第16组解： 0/解/40/96/104，第18组解： 0/解/48/90/102.
应该是37+19=56组。

ysr · 发表于 2021-2-15 21:52

这4组解中的弦长z都超过了100，可能人家不按100内的计算的。如果说x+y=140内的整数的解，应该算上的。

费尔马1 · 发表于 2021-2-15 21:58

已知a^2+b^2=c^2，且a+b=k问a、b、c有多少组正整数解并写出这些解？
解:a+b=k，令k有n个素因子，且每个素因子都能表示为a+b。
猜想:a、b、c正整数解的组数是:
C(n,1)*2^0+C(n,2)*2^1+C(n,3)*2^2+C(n,4)*2^3+C(n,5)*2^4+……+C(n,i)*2^(i－1)+……+C(n,n)*2^(n－1)。
其中，C(n,i)表示从n个元素中取出i个元素的组合数。
我验证了a+b=k=7*17*23*31*41*47=163500169
对于猜想成立！由此可以初步判断猜想很可能是成立的！
请老师们继续探讨！谢谢！

ysr · 发表于 2021-2-15 22:11

163500169=7*17*23*31*41*47，你的公式是怎么算的?二项式系数再乘以2的n次方？
这个数的勾股数解还没有算出来呢，是说的x+y=163500169吗？
3个多小时块4个小时了，明早再看结果吧！

费尔马1 · 发表于 2021-2-15 22:21

已知a^2+b^2=c^2，且a+b=7*17*23*31*41*47=163500169
问a、b、c有多少组正整数解并写出这些解？
解:其解数是，C(6,1)*2^0+C(6,2)*2^1+C(6,3)*2^2+C(6,4)*2^3+C(6，5)*2^4+C(6,6)*2^5
=6*1+15*2+20*4+15*8+6*16+1*32=364(组)
请老师们验证！

ysr · 发表于 2021-2-16 00:06

好几个小时了，还没有出来结果，数据大了，还没有穷举法快？
我再用穷举法试试，看看几个小时出来，现在是为晚上12：10，开始运行程序！

ysr · 发表于 2021-2-16 00:12

穷举法快，5分钟就出来了：（结果是否对呢？仅供参考）

有447组解： 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ysr · 发表于 2021-2-16 00:21

结果好像不对，数据大程序判断出问题了，可能是其中的大数值出现了科学记数法的缘故，已经改进，重新计算一下吧！

ysr · 发表于 2021-2-16 00:29

本帖最后由 ysr 于 2021-2-15 16:30 编辑

出来了，咋才9组解呢？
有9组解： /解/0/163500169/163500169/解/1/163500168/163500168/解/40451584/123048585/129527159/解/43566249/119933920/127601580/解/45679104/117821065/126366071/解/47341295/116158874/125435570/解/52464676/111035493/122806445/解/65727100/97773069/117811819/解/80080106/83420063/115636198
验证个小数值：有5组解： /解/0/10001/10001/解/1197/8804/8885/解/1820/8181/8381/解/3836/6165/7261/解/4745/5256/7081（这个是对的，咋回事呢？）

还是不对？
代码如下：
Private Sub Command1_Click()
Dim x, y, z
m = Text2
x = 0
Do While x < Val(m) / 2 + 1

y = Val(m) - x
z = Int(Sqr(x ^ 2 + y ^ 2))
If x ^ 2 + y ^ 2 - z ^ 2 = 0 Then
s = s & "/解/" & x & "/" & y & "/" & z
s1 = s1 + 1
Else
s = s
End If
x = x + 1
Loop

Text1 = Text1 & "有" & s1 & "组解： " & s
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""

End Sub

晚安，明天看另一个程序的结果吧！

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