Jacobi–Madden equation

The Jacobi–Madden equation is the Diophantine equation

${\displaystyle a^{4}+b^{4}+c^{4}+d^{4}=(a+b+c+d)^{4},}$

proposed by the physicist Lee W. Jacobi and the mathematician Daniel J. Madden in 2008. The variables a, b, c, and d can be any integers, positive, negative or 0. Jacobi and Madden showed that there are an infinitude of solutions of this equation with all variables non-zero.