*inter alia*, that at least n powers of positive integers are needed to get a sum which is a n-th power as well.

It is up to you to find a set of integers {a,b,c,d,e} such that

**a^5+b^5+c^5+d^5=e^5**.

REM: If unable to provide a proof, present the current state of known solutions for 4th and 5th powers. AFAIK no solution for the 6th power exists so far.