<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we show that the Diophantine equation<italic>a</italic><italic>x</italic> +(<italic>a</italic> +2)<italic>y</italic> = <italic>z</italic>2,where <italic>a</italic> ≡ 5 (mod 42) and <italic>a</italic> ∈ ℕ has no solution in non-negative integers.</abstract>

In this paper, we show that the Diophantine equationax +(a +2)y = z2,where a ≡ 5 (mod 42) and a ∈ ℕ has no solution in non-negative integers.

On the Diophantine Equation <italic>a</italic><italic>x</italic> +(<italic>a</italic> +2)<italic>y</italic> = <italic>z</italic>2 Where <italic>a</italic> ≡ 5 (mod 42)

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Diophantine Equation  +( +2) =  Where  ≡ 5 (mod 42)

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

Published Online: Dec 31, 2020

Page range: 39 - 42

Received: Oct 07, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0030

Keywords
Diophantine equation

© 2020 Rakporn Dokchann et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Dec 31, 2020

Page range: 39 - 42

Received: Oct 07, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0030

KeywordsDiophantine equation

© 2020 Rakporn Dokchann et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Keywords
Diophantine equation