Piotr Miska

activity

20142025

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23 citations · 50 across the 24 of their papers we have counts for

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7 papers · 1 filter

math.NT2022★ 3 cited

On continued fraction partial quotients of square roots of primes

Vítězslav Kala, Piotr Miska

We show that for each positive integer $a$ there exist only finitely many prime numbers $p$ such that $a$ appears an odd number of times in the period of continued fraction of $\sq…

math.NT2022

Characteristics of distributions of sets and their $(R)$ - and $(N)$ -denseness

Piotr Miska, János T. Tóth

Let $0 \leq q \leq 1$ and $N$ denotes the set of all positive integers. In this paper we will deal with it too the family $U (x^{q})$ of all regularly distributed set…

math.NT2022

On Frobenius problem with restrictions on common divisors of coefficients

Piotr Miska, Maciej Zakarczemny

Let $m, s, t$ are positive integers with $t \leq s - 2$ and $a_{1}, a_{2}, \dots, a_{s}$ are positive integers such that $(a_{1}, a_{2}, \dots, a_{s - 1}) = 1$ . In the paper we prove that every sufficien…

math.AC2022★ 2 cited

On Waring numbers of henselian rings

Tomasz Kowalczyk, Piotr Miska

Let $n > 1$ be a positive integer. Let $R$ be a henselian local ring with residue field $k$ of $n$ th level $s_{n} (k)$ . We give some upper and lower bounds for the $n$ th Waring number $…

math.NT2022

On the Diophantine equation $σ_{2} (X_{n}) = σ_{n} (X_{n})$

Piotr Miska, Maciej Ulas

In this note we investigate the set $S (n)$ of positive integer solutions of the title Diophantine equation. In particular, for a given $n$ we prove boundedness of the number of sol…

math.NT2022

Binomial coefficients, roots of unity and powers of prime numbers

Piotr Miska

Let $t \in N_{+}$ be given. In this article we are interested in characterizing those $d \in N_{+}$ such that the congruence $$\frac{1}{t}\sum_{s=0}^{t-1}{n+dζ_t^s\choose…

math.NT2022

$p$ -Adic quotient sets: diagonal forms

Deepa Antony, Rupam Barman, Piotr Miska

For a set of integers $A$ , we consider $R (A) = {a / b : a, b \in A, b \neq = 0}$ . It is an open problem to study the denseness of $R (A)$ in the $p$ -adic numbers when $A$ is the set of non…

On continued fraction partial quotients of square roots of primes

Characteristics of distributions of sets and their (R)- and (N)-denseness

On Frobenius problem with restrictions on common divisors of coefficients

On Waring numbers of henselian rings

On the Diophantine equation σ2​(Xn​)=σn​(Xn​)

Binomial coefficients, roots of unity and powers of prime numbers

p-Adic quotient sets: diagonal forms

Characteristics of distributions of sets and their $(R)$ - and $(N)$ -denseness

On the Diophantine equation $σ_{2} (X_{n}) = σ_{n} (X_{n})$

$p$ -Adic quotient sets: diagonal forms