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

Attila Bérczes

Attila Bérczes

University of Debrecen, Institute of MathematicsDebrecen, Hungary
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Bérczes, Attila
, 
Maohua Le

Maohua Le

Institute of Mathematics, Lingnan Normal College ZhangjiangGuangdong, China
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Le, Maohua
, 
István Pink

István Pink

University of Debrecen, Institute of MathematicsDebrecen, Hungary
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Pink, István
 and 
Gökhan Soydan

Gökhan Soydan

Department of Mathematics, Bursa Uludağ UniversityBursa, Turkey
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Soydan, Gökhan
  
Jul 08, 2021
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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
© 2021 Attila Bérczes et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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.

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English
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Mathematics, General Mathematics
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