Pythagorean Triples

PYTHAGOREAN TRIPLES MONDAY, OCTOBER 11, 2010 According to the website link, www.math.uic.edu/~fields/puzzle/triples.html, there is a formula that can find all pythagorean triples--n2 - m2, 2mn, and n2 + m2 (www.math.uic.edu. All pythagorean triples follow the a2 + b2 = c2. Wolfram MathWorld gives their definition of a pythagorean triple as "a triple of positive integers a, b, and c such that a right triangle exists with legs a, b, and hypotenuse c (mathworld.wolfram.com). It is also equivalent to finding positive integers a, b, and c that satisfy a^2+b^2=c^2 (www.math.uic.edu). The website, www.cut-the-knot.org/pythagoras/pythTriple.shtml, gives proof of the three number a, b, and c that always form a Pythagorean triple: (n2 - m2)2 + (2mn)2 = n4 - 2n2m2 + m4 + 4n2m2 = n4 + 2n2m2 + m4 = (n2 + m2)2 (www.cut-the-knot.org). Resources Pythagorean Triples, www.math.uic.edu/~fields/puzzle/triples.html Pythagorean Triple -- from Wolfram MathWorld. mathworld.wolfram.com Pythagorean Triples www.cut-the-knot.org/pythagoras/pythTriple.shtml