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

On equal values of power sums of arithmetic progressions

András Bazsó   ORCID icon 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

Puni tekst: engleski, pdf (130 KB) str. 253-263 preuzimanja: 216* citiraj
APA 6th Edition
Bazsó, A., Kreso, D., Luca, F. i Pintér, Á. (2012). On equal values of power sums of arithmetic progressions. Glasnik matematički, 47 (2), 253-263. https://doi.org/10.3336/gm.47.2.02
MLA 8th Edition
Bazsó, András, et al. "On equal values of power sums of arithmetic progressions." Glasnik matematički, vol. 47, br. 2, 2012, str. 253-263. https://doi.org/10.3336/gm.47.2.02. Citirano 25.10.2021.
Chicago 17th Edition
Bazsó, András, Dijana Kreso, Florian Luca i Ákos Pintér. "On equal values of power sums of arithmetic progressions." Glasnik matematički 47, br. 2 (2012): 253-263. https://doi.org/10.3336/gm.47.2.02
Harvard
Bazsó, A., et al. (2012). 'On equal values of power sums of arithmetic progressions', Glasnik matematički, 47(2), str. 253-263. https://doi.org/10.3336/gm.47.2.02
Vancouver
Bazsó A, Kreso D, Luca F, Pintér Á. On equal values of power sums of arithmetic progressions. Glasnik matematički [Internet]. 2012 [pristupljeno 25.10.2021.];47(2):253-263. https://doi.org/10.3336/gm.47.2.02
IEEE
A. Bazsó, D. Kreso, F. Luca i Á. Pintér, "On equal values of power sums of arithmetic progressions", Glasnik matematički, vol.47, br. 2, str. 253-263, 2012. [Online]. https://doi.org/10.3336/gm.47.2.02

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
https://hrcak.srce.hr/93939

Posjeta: 426 *