Primitive Pythagorean triples

Primitive Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean theorem, which states that in a right triangle, the square of the longest side (hypotenuse, c) is equal to the sum of the squares of the other two sides (a and b). A primitive triple specifically has no common factors other than 1, meaning a, b, and c are coprime. An example is (3, 4, 5). These triples are important in mathematics and geometry for understanding relationships between side lengths in right-angled triangles.