I have almost no idea how to start! I'm just doing this problem for fun(or was at one time):(adsbygoogle = window.adsbygoogle || []).push({});

Find all a such that the equation x^2+axy+y^2=1 has infinitely many solutions in integers for x and y. I know that the solution of this problem would follow from a complete understanding of integer squares of the form (b^2-4)(c^2-4) for integers b and c. If I could achieve an understanding of expressions of this form, I could solve the problem. What are your thoughts on this problem?

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# Interesting number theory-related problem.

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