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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: 479* citiraj
APA 6th Edition
Bauer, M. i Bennett, M.A. (2015). SQUARES FROM SUMS OF FIXED POWERS. Glasnik matematički, 50 (2), 279-288. https://doi.org/10.3336/gm.50.2.03
MLA 8th Edition
Bauer, Mark i Michael A. Bennett. "SQUARES FROM SUMS OF FIXED POWERS." Glasnik matematički, vol. 50, br. 2, 2015, str. 279-288. https://doi.org/10.3336/gm.50.2.03. Citirano 27.10.2021.
Chicago 17th Edition
Bauer, Mark i Michael A. Bennett. "SQUARES FROM SUMS OF FIXED POWERS." Glasnik matematički 50, br. 2 (2015): 279-288. https://doi.org/10.3336/gm.50.2.03
Harvard
Bauer, M., i Bennett, M.A. (2015). 'SQUARES FROM SUMS OF FIXED POWERS', Glasnik matematički, 50(2), str. 279-288. https://doi.org/10.3336/gm.50.2.03
Vancouver
Bauer M, Bennett MA. SQUARES FROM SUMS OF FIXED POWERS. Glasnik matematički [Internet]. 2015 [pristupljeno 27.10.2021.];50(2):279-288. https://doi.org/10.3336/gm.50.2.03
IEEE
M. Bauer i M.A. Bennett, "SQUARES FROM SUMS OF FIXED POWERS", Glasnik matematički, vol.50, br. 2, str. 279-288, 2015. [Online]. https://doi.org/10.3336/gm.50.2.03

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

Posjeta: 676 *