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Compute the number of positive integer ordered pairs $(a, b)$ so that $x^a + y^a$ is divisible by $x^b + y^b$ whenever $x, y$ are coprime positive integers.

Can someone explain to me clearly how one arrives at the conclusion: There should be an infinite amount, as $a\equiv1\pmod2$ and $b=1$ will always work.

I understand it sort of, in that undefined way you know a word but don't really.

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It comes from the formula $$x^n+y^n=(x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y^2-...-xy^{n-2}+y^{n-1})$$

whenever $n$ is odd.

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