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

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2 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.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…