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Yearly Diophantine Puzzle (Posted on 2015-06-12) Difficulty: 3 of 5
Each of A and B (with A ≤ B) is a divisor of 2016.
For how many pairs (A, B) do A2 + B2 equal a perfect square?

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 1 of 1
The 24 sets of A, B and C where A^2 + B^2 = C^2:

3 4 5
6 8 10
7 24 25
9 12 15
12 16 20
14 48 50
16 63 65
18 24 30
21 28 35
21 72 75
24 32 40
28 96 100
32 126 130
36 48 60
42 56 70
42 144 150
63 84 105
72 96 120
84 112 140
84 288 300
126 168 210
168 224 280
252 336 420
504 672 840

DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For a = 1 To 2016
   If 2016 Mod a = 0 Then
     For b = a To 2016
       If 2016 Mod b = 0 Then
         c2 = a * a + b * b
         c = Int(Sqr(c2) + 0.5)
         If c * c = c2 Then
           Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf
           ct = ct + 1
         End If
       End If
     Next b
   End If
 Next a

 
 Text1.Text = Text1.Text & ct & crlf & " done"
  
End Sub


  Posted by Charlie on 2015-06-12 15:23:04
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