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https://doi.org/10.3336/gm.50.2.03

SQUARES FROM SUMS OF FIXED POWERS

Mark Bauer ; Department of Mathematics, University of Calgary, Calgary, AB, Canada
Michael A. Bennett ; Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada


Puni tekst: engleski pdf 120 Kb

str. 279-288

preuzimanja: 678

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Sažetak

In this paper, we show that if p and q are positive integers, then the polynomial exponential equation px+qx=y2 can have at most two solutions in positive integer x and y. If such solutions exists, we are able to precisely characterize them. Our proof relies upon a result of Darmon and Merel, and Chabauty's method for finding rational points on curves of higher genus.

Ključne riječi

Diophantine equations; Chabauty's method

Hrčak ID:

150131

URI

https://hrcak.srce.hr/150131

Datum izdavanja:

29.12.2015.

Posjeta: 1.055 *