Thread: Show that if (a,m) = 1 and m has a prime factor p such that (p-1) | Q, then (a^Q-1,m)

Show that if (a,m) = 1 and m has a prime factor p such that (p-1) | Q, then

I am not sure how to do this, so any help would be great!

since p divides m, if we show that ,then the statement is proved.
since p-1 divides Q, there exist integer k such that Q=(p-1)k.
by the fermat theorem: ;
and
thus p divides . QED