14 citations · 14 across the 6 of their papers we have counts for
6 papers · 1 filter
On a character-twisted analogue of Schäffer's equation
Kálmán Györy, Vandita Patel, Ákos Pintér +1
Let be a positive integer, and let be a primitive quadratic character of conductor . Let be a positive integer, and write for the -th Bernoulli polynom…
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 power values of pyramidal numbers, II
Andrej Dujella, Kálmán Győry, Philippe Michaud-Jacobs +1
For , we define the th order pyramidal number by \[ \mathrm{Pyr}_m(x) = \frac{1}{6} x(x+1)((m-2)x+5-m). \] In a previous paper, written by the first-, second-, and fou…
Another generalization of a theorem of Baker and Davenport
Bo He, Ákos Pintér, Alain Togbe +1
Dujella and Pethő, generalizing a result of Baker and Davenport, proved that the set cannot be extended to a Diophantine quintuple. As a consequence of our main result,…
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 + \…
On Arithmetic Progressions in Recurrences - A new characterization of the Fibonacci sequence
Akos Pinter, Volker Ziegler
We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear re…