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.

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