M. Gawron

activity

20142017

collaborators

5 papers

math.NT2017

Arithmetic properties of coefficients of power series expansion of $\prod_{n = 0}^{\infty} (1 - x^{2^{n}})^{t}$ (with an Appendix by Andrzej Schinzel)

Maciej Gawron, Piotr Miska, Maciej Ulas

Let $F (x) = \prod_{n = 0}^{\infty} (1 - x^{2^{n}})$ be the generating function for the Prouhet-Thue-Morse sequence $((- 1)^{s_{2} (n)})_{n \in N}$ . In this paper we initiate the study of the…

math.CO2016

On formal inverse of the Prouhet-Thue-Morse sequence

Maciej Gawro, Maciej Ulas

Let $p$ be a prime number and consider a $p$ -automatic sequence $u = (u_{n})_{n \in N}$ and its generating function $U (X) = \sum_{n = 0}^{\infty} u_{n} X^{n} \in F_{p} [[X]]$ . M…

math.NT2015

On decompositions of quadrinomials and related Diophantine equations

Maciej Gawron

Let $A, B, C, D$ be rational numbers such that $A B C \neq = 0$ , and let $n_{1} > n_{2} > n_{3} > 0$ be positive integers. We solve the equation $A x^{n_{1}} + B x^{n_{2}} + C x^{n_{3}} + D = f (g (x)),$ in $f,g \…

math.NT2015

On primitive integer solutions of the Diophantine equation $t^{2} = G (x, y, z)$ and related results

Maciej Gawron, Maciej Ulas

In this paper we investigate Diophantine equations of the form $T^{2} = G (X), X = (X_{1}, \dots, X_{m})$ , where $m = 3$ or $m = 4$ and $G$ is specific homogenous quint…

math.CO2014

A note on the arithmetic properties of Stern Polynomials