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arXiv · 1910.08255

An analogue of Ruzsa's conjecture for polynomials over finite fields

Jason P. Bell·Khoa D. Nguyen
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Abstract

In 1971, Ruzsa conjectured that if $f:\ \mathbb{N}\rightarrow\mathbb{Z}$ with $f(n+k)\equiv f(n)$ mod $k$ for every $n,k\in\mathbb{N}$ and $f(n)=O(\theta^n)$ with $\theta<e$ then $f$ is a polynomial. In this paper, we investigate the analogous problem for the ring of polynomials over a finite field.

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Jason P. Bell, Khoa D. Nguyen. 2019-10-18. An analogue of Ruzsa's conjecture for polynomials over finite fields. https://arxiv.org/abs/1910.08255

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