On some arithmetic conditions of recurrent sequences modulo prime p

Ilya Vyugin; Sashadhar Dutta

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arXiv · 2605.24146

On some arithmetic conditions of recurrent sequences modulo prime p

Ilya Vyugin·Sashadhar Dutta

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Abstract

We study the $K$-Fibonacci sequence $\mathcal{F}_p$ modulo prime $p$. Cardinalities of sets $|\mathcal{F}_p+\mathcal{F}_p|$ and $|\mathcal{F}_p\cdot\mathcal{F}_p|$ are estimated. We present the method of estimating doubling constant of some $m$-dimensional recurrent sets in $\mathbb{F}_p$.

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Ilya Vyugin, Sashadhar Dutta. 2026-05-22. On some arithmetic conditions of recurrent sequences modulo prime p. https://arxiv.org/abs/2605.24146

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