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A Pythagorean triple consists of three positive integers a, b, and c, such that a^{2} + b^{2} = c^{2}. Such a triple is commonly written (a, b, c), and a wellknown example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple (PPT) is one in which a, b and c are pairwise coprime. A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle.
The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a^{2} + b^{2} = c^{2}; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with noninteger sides do not form Pythagorean triples. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 do not have an integer common multiple because √2 is irrational. There are 16 primitive Pythagorean triples with c ≤ 100:
Each one of these lowc points forms one of the more easilyrecognizable radiating lines in the scatter plot.
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