Glasnik matematički, Vol. 50 No. 2, 2015.
Original scientific paper
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
Abstract
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.
Keywords
Diophantine equations; Chabauty's method
Hrčak ID:
150131
URI
Publication date:
29.12.2015.
Visits: 1.110 *