Type: Article

On equal values of power sums of arithmetic progressions

Bazso, Andras; Kreso, Dijana; Luca, Florian; et. al.;

Abstract:

In this paper, we consider the Diophantine equation b(k) + (a + b)(k) + ... + (a (x - 1) + b)(k) = = d(l) + (c + d)(l) + ... + (c (y - 1) + d)(l), where a, b, c, d, k, l are given integers with gcd (a, b) = gcd (c, d) = 1, k not equal l. We prove that, under some reasonable assumptions, the above equation has only finitely many solutions