Let R be a UFD, a in R*\U(R), a =p_1^(a_1).......p_t^(a_t) for distinct non-associated primes p_j, (a_j) >= 1, 1=<j=<t.
If d|a the show that d~p_1^(b_1).....p_t^(b_t) for some 0=<b_j=<a_j, 1=<j=<t.
Show that there are (1+a_1)....(1+a_t) distinct ideals (d) such that (a)=< (d). Deduce that R satisfies ascending chain condition (ACC) on principal ideals.
I dont know how to do this question, please help