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.


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.