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
Sum of two squares theorem Sum of two squares theorem In number theory, the sum of two squares theorem says when an integer can be written as a sum of two squares, that is, when for some integers , . This theorem supplements Fermat's two-square theorem which says when a prime number can be written as a sum of two squares, in that it also covers the case for composite numbers. The prime decomposition of the number 2450 is given by 2450 = 257. Of the primes occurring in this decomposition, 2, 5, and 7, only 7 is congruent to 3 modulo 4. Its exponent