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 Simultaneous Pythagorean Poser 2 (Posted on 2015-09-05)
Find all possible triplets (A, B, C) of positive integers, with A ≤ B, that satisfy this system of equations:

A2 + B2 = C2, and

A+B = 2C - 99

 No Solution Yet Submitted by K Sengupta No Rating

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 corrected computer solution Comment 4 of 4 |
(In reply to Solution, with thanks to the classical Greeks by xdog)

`  a   b      c 15 112   113 27 120   123 55 132   143 72 135   153 84 135   159 99 132   165119 120   169`

Two more solutions appear than in xdog's solution: the first and the last.

DefDbl A-Z

Dim crlf\$

Form1.Visible = True

Text1.Text = ""

crlf = Chr\$(13) + Chr\$(10)

For tot = 2 To 50000

For a = 1 To tot / 2

b = tot - a

c = (a + b + 99) / 2

If c = Int(c) And a * a + b * b = c * c Then

Text1.Text = Text1.Text & a & Str(b) & "   " & c & crlf

DoEvents

End If

Next

Next

Text1.Text = Text1.Text & crlf & " done"

End Sub

 Posted by Charlie on 2015-09-06 08:46:20

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