Value sets of non-permutation polynomials over the residue class rings of integers

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发表日期：

2025年4月16日

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Shikui Shang

摘要

In this paper, we study the value sets of non-permutation polynomial functions over the residue class ring $\mathbb {Z}/m\mathbb {Z}$ $Z / m Z$ . When $m=p^r$ $m = p^{r}$ is a power of some prime p, an upper bound is given for the size of the value set of a polynomial function which is not a permutation. We also show that this upper bound can be achieved by some integral polynomials. Finally, we generalize the results for any positive integer m with known prime decomposition.