A **Pythagorean triple** consists of three positive , *b*, and *c*, such that *a*^{2} + *b*^{2} = *c*^{2}. 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 integeis derived from the, stating that everyhas 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 non-integer sides do not form Pythagorean triples. For 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 irrationalr *k*. A **primitive Pythagorean triple** is one in which *a*, *b* and *c* are triangle whose sides form a Pythagorean triple is called a **Pythagorean triang**The name

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