Find all possible pairs (p, q) of positive integers, with p ≤ q, such that (q² + 1)/(pq - 1) is an integer.

I ended up creating the following in Visual Basic, through Excel, and got three possible pairs for P and Q:

1     2
1     3
2     3

Sub Integer_Pairs()
    Listings = ""
    For P = 1 To 100
        If P = 1 Then Min = 2 Else Min = P
        For Q = Min To 100
            If ((Q * Q + 1) Mod (P * Q - 1)) = 0 Then Listings = Listings + Str(P) + "     " + Str(Q) + Chr(10)
        Next
    Next
    MsgBox (Listings)
End Sub

Posted by Justin on 2009-12-25 19:52:20