Mikhail R. Gabdullin

collaborators

3 papers

math.NT2023

Long strings of consecutive composite values of polynomials

Kevin Ford, Mikhail R. Gabdullin

We show that for any polynomial $f$ from the integers to the integers, with positive leading coefficient and irreducible over the rationals, if $x$ is large enough then there is a…

math.NT2023

Karatsuba's divisor problem and related questions

Mikhail R. Gabdullin, Vitalii V. Iudelevich, Sergei V. Konyagin

We prove that $p \leq x \sum \frac{1}{τ ( p - 1 )} ≍ \frac{x}{( lo g x ) ^{3/2}}, n \leq x \sum \frac{1}{τ ( n ^{2} + 1 )} ≍ \frac{x}{( lo g x ) ^{1/2}},$ where $τ(n)=\s…

math.NT2016

Set avoiding squares in $Z_{m}$

Mikhail Gabdullin

We prove that for all squarefree $m$ and any set $A \subset Z_{m}$ such that $A - A$ does not contain non-zero squares the bound $∣ A ∣ \leq m^{1/2} (3 n)^{1.5 n}$ holds, where $n$ de…

Long strings of consecutive composite values of polynomials

Karatsuba's divisor problem and related questions

Set avoiding squares in Zm​

Set avoiding squares in $Z_{m}$