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· 2013 · math.NT · arXiv 1312.1166

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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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math.NT 1

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2026 1

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UNVERDICTED 1

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  • Positive density for Sun's $2^k+m$ conjecture math.NT · 2026-05-15 · unverdicted · none · ref 14 · internal anchor

    The set of n > 1 satisfying Sun's 2^k + m representation property has positive lower density at least 0.0734.