Original scientific paper

https://doi.org/10.3336/gm.47.2.02

On equal values of power sums of arithmetic progressions

András Bazsó orcid.org/0000-0002-9956-1152 ; Institute of Mathematics, MTA-DE Research Group "Equations, functions and curves", Hungarian Academy of Science, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
Dijana Kreso ; Institut für Mathematik (A), Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria
Florian Luca ; Mathematical Center UNAM, UNAM Ap. Postal 61-3 (Xangari), CP 58 089, Morelia, Michoacán, Mexico
Ákos Pintér ; Institute of Mathematics, MTA-DE Research Group "Equations, functions and curves", Hungarian Academy of Science , University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary

Abstract

In this paper, we consider the Diophantine equation bk +(a+b)k + ··· + (a(x-1) + b)k= dl + (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 ą l. We prove that, under some reasonable assumptions, the above equation has only finitely many solutions.

Keywords

Diophantine equations; exponential equations; Bernoulli polynomials

Hrčak ID:

93939

URI

https://hrcak.srce.hr/93939

Publication date:

19.12.2012.

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