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When is a monic integer polynomial the characteristic polynomial of a non-negative integer m...

Suppose $P(x)$ is a monic integer polynomial with roots $r_1, ... r_n$ such that $p_k = r_1^k + ... + r_n^k$ is a non-negative integer for all positive integers $k$. Is $P(x)$ necessarily the charact …
Qiaochu Yuan's user avatar