It is known that there is no solution in N to
x^5 + y^5 = z^5 (FLT),
but there is a solution to
x^5 + y^5 + u^5 + v^5 = w^5
This was the first counterexample to Euler's conjecture.
What about sum of three fifth powers
x^5 + y^5 + z^5 = t^5
Does a solution exist? Could someone please say something about this case? Thank you.