M. Ulas

activity

20072023

most citedSome observations and speculations on partitions into

d

-th powers

9 citations · 23 across the 38 of their papers we have counts for

collaborators

49 papers

math.NT2023

Geometric progressions in the sets of values of rational functions

Maciej Ulas

Let $a, Q\in\Q$ be given and consider the set $G (a, Q) = {a Q^{i} : i \in N}$ of terms of geometric progression with 0th term equal to $a$ and the quotient $Q$ . Let $f\in\Q(x,…

math.NT2022★ 1 cited

Values of binary partition function represented by a sum of three squares

Bartosz Sobolewski, Maciej Ulas

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…

math.NT2022

Solutions of certain meta-Fibonacci recurrences

Bartosz Sobolewski, Maciej Ulas

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)…

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

Signs behaviour of sums of weighted numbers of partitions

Filip Gawron, Maciej Ulas

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,…

math.NT2021

A Fibonacci type sequence with Prouhet-Thue-Morse coefficients

Eryk Lipka, Maciej Ulas

Let $t_{n} = (- 1)^{s_{2} (n)}$ , where $s_{2} (n)$ is the sum of binary digits function. The sequence $(t_{n})_{n \in N}$ is the well-known Prouhet-Thue-Morse sequence. In this note we…

Geometric progressions in the sets of values of rational functions

Values of binary partition function represented by a sum of three squares

Solutions of certain meta-Fibonacci recurrences

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

Signs behaviour of sums of weighted numbers of partitions

A Fibonacci type sequence with Prouhet-Thue-Morse coefficients

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