use rearrangement inequality to show that
(a^n)(a+1)/(b+1)+(b^n)(b+1)/(c+1)+(c^n)(c+1)/(a+1)
>= (a^n)(a+1)/(a+1)+(b^n)(b+1)/(b+1)+(c^n)(c+1)/(c+1)
=a^n+b^n+c^n
>=3((a+b+c)/3)^n (by power mean inequality)
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