Given any 6 real numbers a,b,c,d,e,f satisfying a + b + c + d+e+f = 0,
prove that the sum of their cubes is equal to 0 (a3 + b3 + c3 + d3+e3+f3 = 0)
if and only if the sum of their 5th powers is equal to 0
(a5 + b5 + c5 + d5 +e5+f5= 0).