Ancient Numbers Theory Puzzle Solved

Mathematicians have found a way to solve for an infinite number of new solutions to a very old number theory puzzle known as Euler’s Diophantine equation: A⁴B⁴C⁴+D⁴ = (A + B + C + D)⁴. Euler’s Diophantine equation was first studied by the ancient Greek mathematician Diophantus, and there were previously only 88 known solutions to it, mostly consisting of very large numbers. The question was whether there was a way to find proof an infinite number of solutions to this puzzle. Mathematician Daniel J. Madden and retired physicist Lee W. Jacobi found their solution by rewriting the equations to describe a family of elliptical curves. Each set of curves describing a new solution creates a seed for solving any subsequent solutions. Their article, "On a⁴ + b⁴ +c⁴ +d⁴ = (a + b + c + d)⁴" is published in the March issue of American Mathematical Monthly.