14 citations · 15 across the 5 of their papers we have counts for
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Effective results for polynomial values of (alternating) power sums of arithmetic progressions
András Bazsó
We prove effective finiteness results concerning polynomial values of the sums and $$ b^k - \left(a+b\…
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…
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…
On the coefficients of power sums of arithmetic progressions
András Bazsó, István Mező
We investigate the coefficients of the polynomial \[ S_{m,r}^n(\ell)=r^n+(m+r)^n+(2m+r)^n+\cdots+((\ell-1)m+r)^n. \] We prove that these can be given in terms of Stirling numbers o…
On equal values of power sums of arithmetic progressions
A. Bazsó, D. Kreso, F. Luca +1
In this paper we consider the Diophantine equation \begin{align*}b^k +\left(a+b\right)^k &+ \cdots + \left(a\left(x-1\right) + b\right)^k=\\ &=d^l + \left(c+d\right)^l + \cdots + \…