On $a^n+bn$ modulo $m$

Zhi-Wei Sun

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arXiv · 1312.1166

On $a^n+bn$ modulo $m$

Zhi-Wei Sun

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Abstract

Let $a$ and $m>0$ be integers. We show that for any integer $b$ relatively prime to $m$, the set $\{a^n+bn:\ n=1,\ldots,m^2\}$ contains a complete system of residues modulo $m$. We also pose several conjectures for further research; for example, we conjecture that any integer $n>1$ can be written as $k+m$ with $2^k+m$ prime, where $k$ and $m$ are positive integers.

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BibTeX RIS

Zhi-Wei Sun. 2014-02-27. On $a^n+bn$ modulo $m$. https://arxiv.org/abs/1312.1166

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