如何把 1/7 拆分成四个不同单位分数的和，并且四个分母之和为最小？

ysr

王守恩 发表于 2026-1-21 07:43
把 1/n 拆分成两个不同单位分数的和。

\(a(2)=1,\frac{1}{2}=\frac{1}{3}+\frac{1}{6}\)

6  25  {10,15}
需要比较的解的个数为： 4组，额，是从2开始的，6是四组，去掉了一组两个分母相同的就是1/6=1/12+1/12

ysr

程序代码如下：
Private Sub Command1_Click()
Dim n, a As Double
n = Val(Text1)
m = 2 * (n + 1) ^ 2
a = Val(n + 1)
Do While a <= Val(2 * n)
b = Val(2 * n)
Do While b <= Val(n * (n + 1)) And b > a
k = Val(a + b)
c = Val(a * b) / Val(k)
If c = n And k <= m Then
m = k
s = "{" & a & "," & b & "}"
s2 = n & "  " & m & "  " & s & vbCrLf
s3 = s3 + 1
End If

b = Val(b + 1)
Loop
a = Val(a + 1)
Loop

If s3 > 0 Then
Text2 = s2 & "需要比较的解的个数为： " & s3 & "组"
Else
Text2 = "无解"
End If

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""

End Sub