On some arithmetic conditions of recurrent sequences modulo prime p

Ilya Vyugin, Sashadhar Dutta

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. W…