Jacobi–Madden equation
The Jacobi–Madden equation is the Diophantine equation a 4 + b 4 + c 4 + d 4 = ( a + b + c + d ) 4 , {\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.