Pythagorean theorem Pythagorean theorem In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides "a", "b" and "c", often called the "Pythagorean equation": where "c" represents the length of the hypotenuse and "a" and "b" the lengths of the triangle's other two sides. Although it is
Proofs of Fermat's theorem on sums of two squares Proofs of Fermat's theorem on sums of two squares Fermat's theorem on sums of two squares asserts that an odd prime number "p" can be expressed as with integer "x" and "y" if and only if "p" is congruent to 1 (mod 4). The statement was announced by Girard in 1625, and again by Fermat in 1640, but neither supplied a proof. The "only if" clause is easy: a perfect square is congruent to 0 or 1 modulo 4, hence a sum of two squares is congruent to 0, 1, or 2. An odd prime number is congruent to either