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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 66, Issue 3

Issues

On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c

Hemar Godinho / Diego Marques / Alain Togbé
  • Department of Mathematics, Statistics, and Computer Science Purdue University Northwest 1401 S, U.S.421 Westville, IN 46391 USA
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Published Online: 2016-08-23 | DOI: https://doi.org/10.1515/ms-2015-0159

Abstract

In this paper, we find all solutions of the Diophantine equation x2 + C= yn in integers x, y ≥ 1, a, b, c ≥ 0, n ≥ 3, with gcd(x, y) = 1, when C= 2a3b17c and C = 2a13b17c.

MSC 2010: Primary 11D61; 11Y50

Key words: Diophantine equation; primitive divisor theorem

The first author thanks FAP-DF and CNPq-Brazil for financial support.

The second author thanks FEMAT, FAP-DF and CNPq-Brazil for financial support.

The third author was partially supported by Purdue University Northwest.

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About the article


Received: 2012-11-13

Accepted: 2014-01-05

Published Online: 2016-08-23

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 565–574, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0159.

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