Some exponential diophantine equations II: The equationx 2 – Dy 2 =k z for evenk
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 int...
| Published in: | Mathematica Slovaca |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Walter de Gruyter GmbH
2022
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| Subjects: | |
| 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 |
| Summary: | 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 . |
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