Elementary algebra sign). One of the most well-known equations describes Pythagoras' law relating the length of the sides of a right angle triangle: This equation states that formula_44, representing the square of the length of the side that is the hypotenuse (the side opposite the right angle), is equal to the sum (addition) of the squares of the other two sides whose lengths are represented by formula_45 and formula_46. An equation is the claim that two expressions have the same value and are equal. Some equations are true for all values of the involved variables (such as formula_47); such equations are called
Legendre's three-square theorem Legendre's three-square theorem In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers if and only if is not of the form formula_2 for integers and . The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as formula_2) are Pierre de Fermat gave a criterion for numbers of the form 3"a" + 1 to be a sum of three squares essentially equivalent to Legendre's theorem, but did not provide a proof. N. Beguelin noticed in 1774 that every positive