A. Radomskii

works on

additive number theory 1 integer sequences 1 lower bounds 1 romanoff's theorem 1 sumsets 1

From the 1 of 4 linked papers with an AI index.

collaborators

4 papers

math.NT2026

Variants of Romanoff's theorem

Artyom Radomskii

The paper investigates two sequences of positive integers and, under certain conditions, establishes a lower bound on how many integers up to a given size can be expressed as a sum…

math.NT2026

On sums of two squares and a basis of order $2$

Artyom Radomskii

Let $R$ denote the set of integers $n$ that can be represented as the sum $n = x^{2} + y^{2}$ with $(x, y) = 1$ . Let $a$ and $b$ be integers with $a > 0$ , $a ∤ b$ . We show t…

math.NT2026

Sums related to Euler's totient function

Artyom Radomskii

We obtain an upper bound for the sum $\sum_{n \leq N} (a_{n} / I ¨ (a_{n}))^{s}$ , where $I ¨ $ is Euler's totient function, $s \in N$ , and $a_{1}, \dots, a_{N}$ are positive integ…

math.NT2026

Long strings of composite values of polynomials and a basis of order 2

Artyom Radomskii

We show that for any polynomial $f : Z \to Z$ with positive leading coefficient and irreducible over $Q$ , if $N$ is large enough then there are two strings…

Variants of Romanoff's theorem

On sums of two squares and a basis of order 2

Sums related to Euler's totient function

Long strings of composite values of polynomials and a basis of order 2

On sums of two squares and a basis of order $2$