A Pythagorean triple consists of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2. This relationship is derived from the Pythagorean theorem, which applies to right-angled triangles, where c represents the length of the hypotenuse, and a and b are the lengths of the other two sides. The most well-known example of a Pythagorean triple is 3, 4, 5, since 3^2 + 4^2 = 9 + 16 = 25, which equals 5^2. Other examples include 5, 12, 13 and 8, 15, 17. Pythagorean triples can be generated using various formulas, making them a fundamental concept in number theory.