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

  • Hemar Godinho EMAIL logo , Diego Marques and Alain Togbé
From the journal Mathematica Slovaca

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

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.



(Communicated by Stanislav Jakubec)


Acknowledgement

The authors are grateful to the referee for helpful suggestions which improved the article.

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Received: 2012-11-13
Accepted: 2014-1-5
Published Online: 2016-8-23
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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