problem with an inequality

I have seen a theorem:

If a_{1},a_{2},........,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

{(a_{1}+a_{2}+........+a_{n})/n}^{m} ≤ or ≥ {(a_{1}^{m}+a_{2}^{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?

Re: problem with an inequality

Just off the top of my head, but since the change from $\displaystyle \le$ to $\displaystyle \ge$, 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.