On the Diophantine Equation ax +(a +2)y = z2 Where a ≡ 5 (mod 42)

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Open Access

|Dec 2020

Abstract

In this paper, we show that the Diophantine equation

a^x +(a +2)^y = z²,

where a ≡ 5 (mod 42) and a ∈ ℕ has no solution in non-negative integers.

[1] CATALAN, E.: Note extraite d’une lettre adressée à l’éditeur par Mr. E. Catalan, Répétiteur à l’école polytechnique de Paris, Journal für die reine und angewandte Mathematik 27 (1844), 192–192.10.1515/crll.1844.27.192
Search in Google Scholar Back to article
[2] MIHAILESCU, P.: Primary cyclotomic units and a proof of Catalan’s conjecture, Journal für die reine und angewandte Mathematik 572 (2004), 167–196.10.1515/crll.2004.048
Search in Google Scholar Back to article
[3] SUVARNAMANI, A.: Solutions of the Diophantine equation 2x + py = z2, Int.J.Math. Sci. Appl 1 (2011), no. 3, 1415–1419.
Search in Google Scholar Back to article
[4] SROYSANG, B.: On the Diophantine equation 5x+7y = z2, Int. J. Pure Appl. Math. 89 (2013), no. 1, 115–118.10.12732/ijpam.v89i1.14
Search in Google Scholar Back to article
[5] SROYSANG, B.: On the Diophantine equation 47x +49y = z2, Int. J. Pure Appl. Math. 89 (2013), no. 2, 279–282.10.12732/ijpam.v89i2.11
Search in Google Scholar Back to article
[6] SROYSANG, B.: On the Diophantine equation 89x+91y = z2, Int. J. Pure Appl. Math. 89 (2013), no. 2, 283–286.10.12732/ijpam.v89i2.12
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/tmmp-2020-0030 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

Language: English

Page range: 39 - 42

Submitted on: Oct 7, 2019

Published on: Dec 31, 2020

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

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© 2020 Rakporn Dokchann, Apisit Pakapongpun, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.