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On primitive solutions of the Diophantine equation x2 + y2 = M

On primitive solutions of the Diophantine equation x2 + y2 = M AbstractWe provide explicit formulae for primitive, integral solutions to the Diophantine equation x2+y2=M{x}^{2}+{y}^{2}=M, where MMis a product of powers of Pythagorean primes, i.e., of primes of the form 4n+14n+1. It turns out that this is a nice application of the theory of Gaussian integers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

On primitive solutions of the Diophantine equation x2 + y2 = M

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Publisher
de Gruyter
Copyright
© 2021 Chris Busenhart et al., published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2021-0087
Publisher site
See Article on Publisher Site

Abstract

AbstractWe provide explicit formulae for primitive, integral solutions to the Diophantine equation x2+y2=M{x}^{2}+{y}^{2}=M, where MMis a product of powers of Pythagorean primes, i.e., of primes of the form 4n+14n+1. It turns out that this is a nice application of the theory of Gaussian integers.

Journal

Open Mathematics – de Gruyter

Published: Aug 27, 2021

Keywords: Pythagorean primes; Diophantine equation; 11D45; 11D09; 11A41

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