Prove for a and b Natural Numbers: If (a^2+b^2)/(1+ab) = c is a Natural Number, then c is a perfect square.?

I think this was an IMO question.

2020-03-30T03:52:46Z

In all the examples I looked at (larger of a and b up to 20,000), c|a^2 and c|b^2.

2017-04-11T00:37:33.809Z

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