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

Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation <italic>x2</italic> − <italic>y2m</italic> = <italic>zn</italic>, <italic>x, y, z, m, n</italic> ∈ ℕ, gcd(<italic>x, y</italic>) = 1, <italic>m</italic> ≥ 2, <italic>n</italic> ≥ 3.
</abstract>

Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.

A note on the ternary Diophantine equation <italic>x</italic>2 − <italic>y</italic>2<italic>m</italic> = z<italic>n</italic>

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

A note on the ternary Diophantine equation  −  = z

Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special...

A note on the ternary Diophantine equation x² − y²^m = zⁿ

Published Online: Jul 08, 2021

Page range: 93 - 105

Received: Nov 20, 2020

Accepted: Dec 30, 2020

DOI: https://doi.org/10.2478/auom-2021-0020

Keywords
higher Diophantine equation, exponential Diophantine equation, generalized Fermat equation, ternary equation

© 2021 Attila Bérczes et al., published by Sciendo

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

A note on the ternary Diophantine equation x2 − y2m = zn

Published Online: Jul 08, 2021

Page range: 93 - 105

Received: Nov 20, 2020

Accepted: Dec 30, 2020

DOI: https://doi.org/10.2478/auom-2021-0020

Keywordshigher Diophantine equation, exponential Diophantine equation, generalized Fermat equation, ternary equation

© 2021 Attila Bérczes et al., published by Sciendo

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

A note on the ternary Diophantine equation x² − y²^m = zⁿ

Keywords
higher Diophantine equation, exponential Diophantine equation, generalized Fermat equation, ternary equation