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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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Some Thoughts A stop? | Comment 2 of 10 |
I want to check my algebra, but I think a^2+b^2 is a multiple of ab+1 only if a=b=1, and in that case the given quotient indeed is a perfect square.

  Posted by Federico Kereki on 2007-03-24 21:59:14
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