M. Garaev

collaborators

2 papers

math.NT2025

Additive congruences with factorials modulo a prime

Moubariz Z. Garaev, Julio C. Pardo

Let $p$ be a large prime number. We prove that any integer $I^»$ modulo $p$ can be represented in the form $m! n! + i = 1 \sum 47 n_{i}! \equiv I^» (mod p),$ with $\max\{m,n,n_1,\ldot…

math.NT2024

Binary and ternary congruences involving intervals and sets modulo a prime

Moubariz Z. Garaev, Julio C. Pardo, Igor E. Shparlinski

Let $s$ be a fixed positive integer constant, $ε$ be a fixed small positive number. Then, provided that a prime $p$ is large enough, we prove that for any set $\{{\mathca…