# Pythagorean triple

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## Pythagorean triple

[pə‚thag·ə¦rē·ən ′trip·əl]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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A familiar example is a Pythagorean triple (a2+b2=c2).
For this we would use the Pythagorean triples. We propose an elegant solution by adding two Pythagorean triples to obtain a new Pythagorean triple.
Consequently, those dates received some points, but not as many as dates in which the three numbers form a Pythagorean triple, which only happens 50 times a century.
A Pythagorean triple is a set of three integers which occur as the side lengths of a right-angled triangle.
Keywords The Smarandache function, Pythagorean triple, equation, positive integer solutions.
As for a Pythagorean triple (x, y, z) satisfying the relation [x.sup.2] + [y.sup.2] = [z.sup.2], all the triples ([??]x, [??]y, [??]z) will also be solutions, implying [N.sub.p] = 8.(p - 1/2.p - 5/4) = (p-1).(p-5) and [N.sub.p] = 8.(p - 1/2.p - 3/4) = (p - 1).(p - 3), respectively.
Did you know, too, that if you take any Pythagorean triple, such as 3, 4, 5 or 5, 12, 13, and multiply the three numbers, the result is always a multiple of 60?
They have variously interpreted the cryptic columns of numbers, written in the wedge-shaped script called cuneiform, as a trigonometric table or a sophisticated scheme for generating Pythagorean triples. A Pythagorean triple is a set of three whole numbers, a, b, and c, such that a[super]2 + b[super]2 = C[super]2.
The relationship, [a.sup.2] + [b.sup.2] = [c.sup.2] for whole numbers like (3,4,5), is called a Pythagorean Triple. Even with the formula, it has been very difficult to calculate exact triples.
Trial and error with the Pythagorean triple {3,4,5} soon establishes that x = 32 and y = 24.
These two numbers form two parts of a Pythagorean Triple: [39.sup.2] + [80.sup.2] = [89.sup.2].
However, when a, b, c are all integers and obey equation (1), they are referred to as a Pythagorean triple [a, b, c].

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