**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.

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## Comments

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

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