Zobrazeno 1 - 10
of 222
pro vyhledávání: '"Ulas, Maciej"'
Autor:
Ulas, Maciej
In this note we consider the title Diophantine equation from both theoretical as well as experimental point of view. In particular, we prove that for $k=4, 6$ and each choice of the signs our equation has infinitely many co-prime positive integer sol
Externí odkaz:
http://arxiv.org/abs/2402.06567
Autor:
Gawron, Filip, Ulas, Maciej
Let $A$ be a subset of positive integers. For a given positive integer $n$ and $0\leq i\leq n$ let $c_{A}(i,n)$ denotes the number of $A$-compositions of $n$ with exactly $i$ parts. In this note we investigate the sign behaviour of the sequence $(S_{
Externí odkaz:
http://arxiv.org/abs/2401.17386
Autor:
Ulas, Maciej
In this note we present a construction of an infinite family of diagonal quintic threefolds defined over $\Q$ each containing infinitely many rational points. As an application, we prove that there are infinitely many quadruples $B=(B_{0}, B_{1}, B_{
Externí odkaz:
http://arxiv.org/abs/2401.17369
In recent literature concerning integer partitions one can find many results related to both the Bessenrodt-Ono type inequalities and log-concavity property. In this note we offer some general approach to this type of problems. More precisely, we pro
Externí odkaz:
http://arxiv.org/abs/2312.14501
Autor:
Ulas, Maciej
Let $a, Q\in\Q$ be given and consider the set $\cal{G}(a, Q)=\{aQ^{i}:\;i\in\N\}$ of terms of geometric progression with 0th term equal to $a$ and the quotient $Q$. Let $f\in\Q(x, y)$ and $\cal{V}_{f}$ be the set of finite values of $f$. We consider
Externí odkaz:
http://arxiv.org/abs/2304.09264
Autor:
Sobolewski, Bartosz, Ulas, Maciej
Let $m$ be a positive integer and $b_{m}(n)$ be the number of partitions of $n$ with parts being powers of 2, where each part can take $m$ colors. We show that if $m=2^{k}-1$, then there exists the natural density of integers $n$ such that $b_{m}(n)$
Externí odkaz:
http://arxiv.org/abs/2211.16622
Autor:
Sobolewski, Bartosz, Ulas, Maciej
In this note we investigate the solutions of certain meta-Fibonacci recurrences of the form $f(n)=f(n-f(n-1))+f(n-2)$ for various sets of initial conditions. In the case when $f(n)=1$ for $n\leq 1$, we prove that the resulting integer sequence is clo
Externí odkaz:
http://arxiv.org/abs/2204.04011
Autor:
Miska, Piotr, Ulas, Maciej
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 solutions, give precise upper bound on the common value of $\sigma_{2}(\o
Externí odkaz:
http://arxiv.org/abs/2203.03942
Autor:
Gawron, Filip, Ulas, Maciej
Let $A$ be a subset of positive integers. By $A$-partition of $n$ we understand the representation of $n$ as a sum of elements from the set $A$. For given $i, n\in\N$, by $c_{A}(i,n)$ we denote the number of $A$-partitions of $n$ with exactly $i$ par
Externí odkaz:
http://arxiv.org/abs/2202.05221
