István Pink

activity

20152024

most citedOn a variant of Pillai's problem

21 citations · 27 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2024

On the largest value of the solutions of Erdős's last equation

István Pink, Csaba Sándor

Let $n$ be a positive integer. The Diophantine equation $n (x_{1} + x_{2} + \dots + x_{n}) = x_{1} x_{2} \dots x_{n}$ , $1 \leq x_{1} \leq x_{2} \leq \dots \leq x_{n}$ is called Erdős's last equation. We prove that…

math.NT2024

Number of solutions to a special type of unit equations in two unknowns, III

Takafumi Miyazaki, István Pink

It is conjectured that for any fixed relatively prime positive integers $a, b$ and $c$ all greater than 1 there is at most one solution to the equation $a^{x} + b^{y} = c^{z}$ in positive int…

math.NT2022★ 1 cited

Number of solutions to a special type of unit equations in two unknowns, II

Takafumi Miyazaki, István Pink

This paper contributes to the conjecture of R. Scott and R. Styer which asserts that for any fixed relatively prime positive integers $a, b$ and $c$ all greater than 1 there is at m…

math.NT2020★ 2 cited

Number of solutions to a special type of unit equations in two variables

Takafumi Miyazaki, István Pink

For any fixed coprime positive integers $a, b$ and $c$ with $min {a, b, c} > 1$ , we prove that the equation $a^{x} + b^{y} = c^{z}$ has at most two solutions in positive integers $x, y$ and $z$ ,…

math.NT2017★ 2 cited

On the Diophantine equation $(x + 1)^{k} + (x + 2)^{k} + ... + (l x)^{k} = y^{n}$

Gökhan Soydan

Let $k, l \geq 2$ be fixed integers. In this paper, firstly, we prove that all solutions of the equation $(x + 1)^{k} + (x + 2)^{k} + ... + (l x)^{k} = y^{n}$ in integers $x, y, n$ with $x,y\geq1, n…

math.NT2016

On a variant of Pillai's problem II

Kwok Chi Chim, István Pink, Volker Ziegler

In this paper, we show that there are only finitely many $c$ such that the equation $U_{n} - V_{m} = c$ has at least two distinct solutions $(n, m)$ , where ${U_{n}}_{n \geq 0}$ and $\{V_…

math.NT2016★ 1 cited

Effective Resolution of Diophantine equations of the form $u_{n} + u_{m} = w p_{1}^{z_{1}} \dots p_{s}^{z_{s}}$

István Pink, Volker Ziegler

Let $u_{n}$ be a fixed non-degenerate binary recurrence sequence with positive discriminant, $w$ a fixed non-zero integer and $p_{1}, p_{2}, \dots, p_{s}$ fixed, distinct prime numbers. In th…

math.NT2016★ 21 cited

On a variant of Pillai's problem

Kwok Chi Chim, István Pink, Volker Ziegler

In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a Tribonacci number.

math.NT2015

Finiteness results for Diophantine triples with repdigit values

Attila Bérczes, Florian Luca, István Pink +1

Let $g \geq 2$ be an integer and $R_{g} \subset N$ be the set of repdigits in base $g$ . Let $D_{g}$ be the set of Diophantine triples with values in $\mathcal R_…

On the largest value of the solutions of Erdős's last equation

Number of solutions to a special type of unit equations in two unknowns, III

Number of solutions to a special type of unit equations in two unknowns, II

Number of solutions to a special type of unit equations in two variables

On the Diophantine equation (x+1)k+(x+2)k+...+(lx)k=yn

On a variant of Pillai's problem II

Effective Resolution of Diophantine equations of the form un​+um​=wp1z1​​⋯pszs​​

On a variant of Pillai's problem

Finiteness results for Diophantine triples with repdigit values

On the Diophantine equation $(x + 1)^{k} + (x + 2)^{k} + ... + (l x)^{k} = y^{n}$

Effective Resolution of Diophantine equations of the form $u_{n} + u_{m} = w p_{1}^{z_{1}} \dots p_{s}^{z_{s}}$