Euler's equation of degree four solved

This post may be a little late(found in march 2008),but i just come across this .One of the unsolved problem proposed by Leonhard Euler in 1772 have a solution now. This problem asks for a solution in integers to the equation a⁴ + b⁴ + c⁴ + d⁴ = (a + b + c + d)⁴.
Mathematician Daniel J. Madden and retired physicist, Lee W. Jacobi, found solutions to a puzzle that has been around for centuries. Please see this link for the complete story. It is very interesting.
This is related to another disproved conjucture of Euler .In 1772, Euler, hypothesized that to satisfy equations with higher powers, there would need to be as many variables as that power. For example, a fourth order equation would need four different variables, like the equation above. Euler's hypothesis was disproved in 1987 by a Harvard graduate student named Noam Elkies. He found a case where only three variables were needed. Elkies solved the equation: (a)(to the fourth power) + (b)(to the fourth power) + (c)(to the fourth power) = e(to the fourth power), which shows only three variables are needed to create a variable that is a fourth power.
95800⁴ + 217519⁴ + 414560⁴ = 422481⁴.