Glasnik matematički, Vol. 47 No. 2, 2012.
Izvorni znanstveni članak
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
Sažetak
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.
Ključne riječi
Diophantine equations; exponential equations; Bernoulli polynomials
Hrčak ID:
93939
URI
Datum izdavanja:
19.12.2012.
Posjeta: 1.178 *