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Arithmetic Properties of Periodic Maps

Zhi-Wei Sun
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Abstract

Let $ψ_1,...,ψ_k$ be periodic maps from $\Bbb Z$ to a field of characteristic p (where p is zero or a prime). Assume that positive integers $n_1,...,n_k$ not divisible by p are their periods respectively. We show that $ψ_1+...+ψ_k$ is constant if $ψ_1(x)+...+ψ_k(x)$ equals a constant for |S| consecutive integers x where S={r/n_s: r=0,...,n_s-1; s=1,...,k}. We also present some new results on finite systems of arithmetic sequences.

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Zhi-Wei Sun. 2004-04-02. Arithmetic Properties of Periodic Maps. https://arxiv.org/abs/math/0402289

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