Some exponential diophantine equations II: The equationx 2 – Dy 2 =k z for evenk

• Published in: Mathematica Slovaca
• Main Authors: Fujita, Yasutsugu, Le, Maohua
• Format: Article in Journal/Newspaper
• Language: English
• Published: Walter de Gruyter GmbH 2022
• Subjects: Evenk
• Online Access: http://dx.doi.org/10.1515/ms-2022-0023; https://www.degruyter.com/document/doi/10.1515/ms-2022-0023/xml; https://www.degruyter.com/document/doi/10.1515/ms-2022-0023/pdf

Abstract Let D be a nonsquare integer, and let k be an integer with | k | ≥ 1 and gcd( D , k ) = 1. In the part I of this paper, using some properties on the representation of integers by binary quadratic primitive forms with discriminant 4 D , M.-H. Le gave a series of explicit formulas for the integer solutions ( x , y , z ) of the equation x 2 – Dy 2 = k z , gcd( x , y ) = 1, z > 0 for 2 ∤ k or | k | is a power of 2. In this part, we give similar results for the other cases of k .