Counting Primitive Pythagorean Triples

Autor/in	Ayoub, Ayoub B.
Titel	Counting Primitive Pythagorean Triples
Quelle	In: Mathematics and Computer Education, 39 (2005) 1, S.37-41 (5 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0730-8639
Schlagwörter	Geometric Concepts; Equations (Mathematics); Mathematical Concepts; Problem Solving; Mathematics Education; Number Concepts + Suchen Sie Ihr Suchwort? Elementare Geometrie; Equations; Mathematics; Gleichungslehre; Problemlösen; Mathematische Bildung; Number concept; Zahlbegriff
Abstract	A triple (x,y,z) of natural numbers is called a Primitive Pythagorean Triple (PPT) if it satisfies two conditions: (1) x[squared] + y[squared] = z[squared]; and (2) x, y, and z have no common factor other than one. All the PPT's are given by the parametric equations: (1) x = m[squared] - n[squared]; (2) y = 2mn; and (3) z = m[squared] + n[squared], where m and n are relatively prime natural numbers, not both odd, and m greater than n. As a result of the constraints imposed on m and n, x will be an odd number, y will be an even number of the form 4l, and z will be an odd number of the form 4k + 1. This article will address the following questions: (1) How many PPT's have the same x?; (2) How many PPT's have the same y?; and (3) How many PPT's have the same z?. As this article will show, the answers depend on the prime factorization of x, y, and z, respectively. (ERIC).
Anmerkungen	MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10