István Pink

activity

20162024

most citedNumber of solutions to a special type of unit equations in two variables

2 citations · 2 across the 2 of their papers we have counts for

collaborators

Showing math.NTShow all

3 papers · 1 filter

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.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.NT2016

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…

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

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

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

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