A note on the ternary Diophantine equation x 2 − y 2 m = z n-Reference-Cited by-同舟云学术

A note on the ternary Diophantine equation x 2 − y 2 m = z n

Published:2021-06-01 Issue:2 Volume:29 Page:93-105
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Bérczes Attila¹,Le Maohua²,Pink István³,Soydan Gökhan⁴

Affiliation:

1. University of Debrecen Institute of Mathematics H-4032 Debrecen , Hungary

2. Institute of Mathematics, Lingnan Normal College Zhangjiang , Guangdong , 524048 China

3. University of Debrecen , Institute of Mathematics H-4032 Debrecen , Hungary

4. Department of Mathematics , Bursa Uludağ University , Görükle Campus, 16059 Bursa , Turkey

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2021-0020

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