A. Radomskii

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20242026

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math.NT2026

Additive complements to the primes and large gaps between Romanoff numbers

Artyom Radomskii

We prove that every set $B \subseteq Z_{\geq 0}$ for which $P + B$ contains all sufficiently large integers satisfies $B (X) ≫ lo g X lo g lo g X$ , whe…

math.NT2026

Long intervals of consecutive composite values of polynomials

Artyom Radomskii

Let $f \in Q [t]$ be an irreducible integer-valued polynomial of positive degree with positive leading coefficient. We show that there is a constant $c_{f} > 0$ such that, for eve…

math.NT2026

Large gaps between Romanoff numbers

Artyom Radomskii

Questions concerning representations of integers as the sum of a prime and a power of two go back to the correspondence between Euler and Goldbach in 1752 and to de Polignac's work…

math.NT2026

A Romanoff-type theorem for a multiset of products of powers

Artyom Radomskii

Let $b_{1}, \dots, b_{d} \geq 2$ be fixed integers, and let $k$ be their multiplicative rank. We study representations $n = a + b_{1}^{u_{1}} \dots b_{d}^{u_{d}}$ , where $a$ belongs to a set $\mathcal{…

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.NT2025

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…

math.NT2024

Sums related to Euler's totient function

Artyom Radomskii

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

Additive complements to the primes and large gaps between Romanoff numbers

Long intervals of consecutive composite values of polynomials

Large gaps between Romanoff numbers

A Romanoff-type theorem for a multiset of products of powers

On sums of two squares and a basis of order 2

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

Sums related to Euler's totient function

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