Glasnik matematički, Vol. 50 No. 1, 2015.
Original scientific paper
https://doi.org/10.3336/gm.50.1.04
A generalization of a problem of Mordell
Bo He
; Institute of Mathematics, Aba Normal University, Wenchuan, Sichuan 623000, P. R. China
Ákos Pintér
; Institute of Mathematics, MTA-DE Research Group "Equations, Functions and Curves", Hungarian Academy of Sciences and University of Debrecen, P. O. Box 12, H-4010 Debrecen, Hungary
Alain Togbé
orcid.org/0000-0002-5882-936X
; Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421, Westville, IN 46391, USA
Nóra Varga
; Institute of Mathematics, MTA-DE Research Group "Equations, Functions and Curves", Hungarian Academy of Sciences and University of Debrecen, P. O. Box 12, H-4010 Debrecen, Hungary
Abstract
In this paper, we use polygonal and pyramidal numbers Polxm and Pyrxm to extend a problem of Mordell. Then we prove that if m≥ 3,n≥ 3 with (m,n)≠ (50,3), (50,6), all the solutions x and y to the related equation verify max(x,y)< C, where C is an effectively computable constant depending only on m and n.
Keywords
Diophantine equation; binomial coefficients; polygonal numbers; pyramidal numbers
Hrčak ID:
140083
URI
Publication date:
15.6.2015.
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