Find all pairs $(x, y)$ of natural numbers such that $$x + y = a^n, x^2 + y^2 = a^m$$for some natural $a, n, m$.
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Tags: number theory, diophantine, system of equations
Find all pairs $(x, y)$ of natural numbers such that $$x + y = a^n, x^2 + y^2 = a^m$$for some natural $a, n, m$.