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# Mathematical Research Letters

## Volume 11 (2004)

### Number 2

### Arithmetic Properties of Periodic Maps

Pages: 187 – 196

DOI: http://dx.doi.org/10.4310/MRL.2004.v11.n2.a4

#### Author

#### Abstract

Let $\psi_1,\ldots,\psi_k$ be periodic maps from $\Z$ to a field of characteristic $p$ (where $p$ is zero or a prime). Assume that positive integers $n_1,\ldots,n_k$ not divisible by $p$ are their periods respectively. We show that $\psi_1+\cs+\psi_k$ is constant if $\psi_1(x)+\cs+\psi_k(x)$ equals a constant for $|S|$ consecutive integers $x$ where $S=\bigcup_{s=1}^k\{r/n_s:\ r=0,\ldots,n_s-1\}$. We also present some new results on finite systems of arithmetic sequences.