12 Feb '10 14:35

Leonard Euler (1707-1783) was inspired of Pierre de Fermat and his x^n + y^n = z^n where n>2 which is now shown to have no solutions in any n. In the case where n=2 solutions was known by Pythagoras.

Euler thought that neither a^5 + b^5 + c^5 + d^5 = e^5 had a solution. Was he right? (a,b,c,d,e are all integers.) He had no computer. We do. But do we know enough to solve the equation without our silicon buddies?

Question:

Solve the equation a^5 + b^5 + c^5 + d^5 = e^5, where a,b,c,d,e are all integers, if possible.

Was Euler wrong?

Euler thought that neither a^5 + b^5 + c^5 + d^5 = e^5 had a solution. Was he right? (a,b,c,d,e are all integers.) He had no computer. We do. But do we know enough to solve the equation without our silicon buddies?

Question:

Solve the equation a^5 + b^5 + c^5 + d^5 = e^5, where a,b,c,d,e are all integers, if possible.

Was Euler wrong?