What Is a Very Hard Math Equation?

An extremely difficult math equation is the Jacobi-Madden equation, a4 + b4 + c4 + d4 = (a + b + c + d)4 where variables a, b, c and d can be any positive integer, negative integer or zero. The Jacobi-Madden equation is considered a Diophantine equation.

The equation was proposed by the physicist Lee Jacobi and mathematician Daniel Madden in 2008. The Jacobi-Madden equation is notable because it represents a solution to the an equation proposed by Leonhard Euler in 1772. The Jacobi-Madden equation proves that there are potentially infinitely many solutions using nonzero integers to the 1772 equation.