The great Euler conjected,
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.
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