Arithmetic Properties of Periodic Maps

Details Arithmetic Properties of Periodic Maps Arithmetic Properties of Periodic Maps

2004-02-18

arxiv.org/abs/math/0402289v2

Mathematics

Number Theory

10 pages; accepted by Math. Res. Lett. Also available from http://pweb.nju.edu.cn/zwsun

Scientific paper

Let $\psi_1,...,\psi_k$ 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 $\psi_1+...+\psi_k$ is constant if $\psi_1(x)+...+\psi_k(x)$ 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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