problem with an inequality

I have seen a theorem:
If a₁,a₂,........,a_n are n positive numbers such that all are not equal, and m is any rational number not equal to 1 and 0,
then
{(a₁+a₂+........+a_n)/n}^m ≤ or ≥ {(a₁^m+a₂^m+........+a_n^m)/n} according as m doesn't or does lie between 0 and 1


I can't find out, when do they get equal?

Just off the top of my head, but since the change from to , and vice-versa, occurs at 0 and 1, I would guess that the only places we could have "=" would be at 0 or 1 or both.