Candido's Identity

Candido's identity, named after the Italian mathematician Giacomo Candido, states that for any two real numbers x and y, the square of the sum of x squared, y squared and the square of x plus y equals twice the sum of x to the fourth power, y to the fourth power and the fourth power of x plus y, an identity that in fact holds in every commutative ring rather than only for real numbers. Candido originally devised it to prove a matching identity for three consecutive Fibonacci numbers.