On pythagorean triples modulo a prime
This paper is an exposition of the article entitled Pythagorean Triples Modulo a Prime by Bernard Moore and Joseph Straight which was published in the Pi Mu Epsilon journal [1]. It discusses the existence and number of solutions to the equation x2 +y2 z2 (mod p), where p is a prime greater than or e...
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| Format: | text |
| Language: | English |
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Animo Repository
2016
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/18395 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | This paper is an exposition of the article entitled Pythagorean Triples Modulo a Prime by Bernard Moore and Joseph Straight which was published in the Pi Mu Epsilon journal [1]. It discusses the existence and number of solutions to the equation x2 +y2 z2 (mod p), where p is a prime greater than or equal to 7 and x, y, and z are elements of the multiplicative group Z#p = f1 2 : : : p {u100000} 1g modulo p. A program was created to compute quadratic residues, siblings of c, distinct values of a and b for a given c to generate Pythagorean triple (a b c) (mod p), Pythagorean triples, quadratic residue, siblings, isosceles Pythagorean triples and number of non-equivalent solutions for prime p. |
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