### Bo He, Ákos Pintér, Alain Togbé and Nóra Varga

Institute of Mathematics, Aba Normal University, Wenchuan, Sichuan 623000, P. R. China
e-mail: bhe@live.cn

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
e-mail: apinter@science.unideb.hu

Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421, Westville, IN 46391, USA
e-mail: atogbe@pnc.edu

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
e-mail: nvarga@science.unideb.hu

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.

2010 Mathematics Subject Classification.   11D41, 11J86, 11B39, 11D61.

Key words and phrases.   Diophantine equation, binomial coefficients, polygonal numbers, pyramidal numbers.

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DOI: 10.3336/gm.50.1.04

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