x+y+z+u=xyzu,有幾組正整數解?

利用 Excel VBA , 程式碼如下:

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Sub my_combination()

M = 100

r = 1

For x = 1 To M

For y = 1 To M

For z = 1 To M

For u = 1 To M

If x + y + z + u = x * y * z * u Then

Cells(r, 1) = x & " " & y & " " & z & " " & u

r = r + 1

End If

Next

Next

Next

Next

End Sub

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執行結果皆為 1 , 1 , 2 , 4 之排列組合

4! / 2! = 24 / 2 = 12

Ans: 12 組正整數解