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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
Published/Copyright: August 23, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 3

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.

(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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https://doi.org/10.1515/ms-2015-0159
Keywords for this article
Diophantine equation; primitive divisor theorem

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  7. Research Article
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  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
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