what is phytagoeran triplet?
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A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2= c2. Such a triple is commonly written (a, b,c), and a well-known 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 is one in which a, b and care 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 a2 + b2 =c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer 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.
The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 =c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer 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.
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