if a+b+c=0 prove (a

^{5}+b

^{5}+c

^{5})/5=abc∗((a

^{2}+b

^{2}+c

^{2})/2)=((a

^{2}+b

^{2}+c

^{2})/2)∗((a

^{3}+b

^{3}+c

^{3})/3)

I can prove it abc∗((abc∗((a

^{2}+b

^{2}+c

^{2})/2)=((a

^{2}+b

^{2}+c

^{2})/2)∗((a

^{3}+b

^{3}+c

^{3})/3) very easy

but i don't know what to do whit (a5+b5+c5)/5 .

I can do this, too: ((a

^{2}+b

^{2}+c

^{2})/2)∗((a

^{3}+b

^{3}+c

^{3})/3)=...=a

^{5}+b

^{5}+c

^{5}−abc(ab+ac+bc)

I will be very thankfull if someone help