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Surprising Sudden Square (Posted on 2007-03-24) Difficulty: 3 of 5
Prove that if a²+b² is a multiple of ab+1, for positive integer a and b, then (a²+b²)/(ab+1) is a perfect square.

No Solution Yet Submitted by Old Original Oskar!    
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re(2): A start | Comment 4 of 10 |
(In reply to re: A start by Brian Smith)

My proof assumed c^2+d^2 wouldn't equal ab+1. It now gives a less powerful result, but still somewhat interesting.

  Posted by Gamer on 2007-03-25 01:50:03

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