<abstract xmlns="http://www.w3.org/1999/xhtml">

Let <italic>m ></italic> 1 be a positive integer. We show that the exponential Diophantine equation <italic>mx</italic> + (<italic>m</italic> + 1)<italic>y</italic> = (1 + <italic>m</italic> + <italic>m</italic>2)<italic>z</italic> has only the positive integer solution (<italic>x, y, z</italic>) = (2, 1, 1) when <italic>m ≥</italic> 2.
</abstract>

Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.

On the exponential Diophantine equation <italic>mx</italic>+(<italic>m</italic>+1)<italic>y</italic>=(1+<italic>m</italic>+<italic>m</italic>2)<italic>z</italic>

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the exponential Diophantine equation +(+1)=(1++)

Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y,...

On the exponential Diophantine equation m^x+(m+1)^y=(1+m+m²)^z

Published Online: Nov 23, 2021

Page range: 23 - 32

Received: Mar 08, 2021

Accepted: Apr 28, 2021

DOI: https://doi.org/10.2478/auom-2021-0032

Keywords
exponential Diophantine equations, Classification Method, primitive divisor theorem

© 2021 Murat Alan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z

Published Online: Nov 23, 2021

Page range: 23 - 32

Received: Mar 08, 2021

Accepted: Apr 28, 2021

DOI: https://doi.org/10.2478/auom-2021-0032

Keywordsexponential Diophantine equations, Classification Method, primitive divisor theorem

© 2021 Murat Alan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the exponential Diophantine equation m^x+(m+1)^y=(1+m+m²)^z

Keywords
exponential Diophantine equations, Classification Method, primitive divisor theorem