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# Merry Christmas

Prove

There exist positive integers $$x$$ and $$y$$ such that $$x^{161}+y^{161}=a^{2}+161b^{2}$$ with $$a$$ and $$b$$ integers, and $$x+y$$ can't be expressed as $$m^{2}+161n^{2}$$ with $$m$$ and $$n$$ also integers.

Note by Jason Snow
9 months, 4 weeks ago

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You may spend lots of time considering two numbers satisfying the conditions above, as a matter of fact, using a few tactics may be helpful

- 9 months, 4 weeks ago