A Pythagorean triple consists of three positive integer

Integer

The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

s a, b, and c, such that . Such a triple is commonly written , and a well-known example is . If 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

Coprime

In number theory, a branch of mathematics, two integers a and b are said to be coprime or relatively prime if the only positive integer that evenly divides both of them is 1. This is the same thing as their greatest common divisor being 1...

. A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle.

The name is derived from the Pythagorean theorem

Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

, stating that every right triangle

Right triangle

A right triangle or right-angled triangle is a triangle in which one angle is a right angle . The relation between the sides and angles of a right triangle is the basis for trigonometry.-Terminology:The side opposite the right angle is called the hypotenuse...

 has side lengths satisfying the formula ; thus, Pythagorean triples describe the three integer side lengths of a right triangle.