<Dd> (x − 1 2) 2 + (x + 1 2) 2 = y 2 (\ displaystyle ((\ tfrac (x-1) (2))) ^ (2) + ((\ tfrac (x + 1) (2))) ^ (2) = y ^ (2)) </Dd> <P> where (x, y) are the solutions to the Pell equation x 2 − 2 y 2 = − 1 (\ displaystyle x ^ (2) - 2y ^ (2) = - 1). </P> <P> When it is the longer non-hypotenuse side and hypotenuse that differ by one, such as in </P> <Dl> <Dd> 5 2 + 12 2 = 13 2 (\ displaystyle 5 ^ (2) + 12 ^ (2) = 13 ^ (2)) </Dd> </Dl>

Sum of the side lengths of a right triangle with sides of integer length