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math.NT2023
Singmaster-type results for Stirling numbers and some related diophantine equations
András Bazsó, István Mező, {Á}kos Pintér +1
Motivated by the work of David Singmaster, we study the number of times an integer can appear among the Stirling numbers of both kinds. We provide an upper bound for the occurrence…
math.NT2023
On equal values of products and power sums of consecutive elements in an arithmetic progression
András Bazsó, Dijana Kreso, Florian Luca +2
In this paper we study the Diophantine equation \begin{align*} b^k + \left(a+b\right)^k + &\left(2a+b\right)^k + \ldots + \left(a\left(x-1\right) + b\right)^k = \\ &y\left(y+c\righ…