I need your help is proving this statement;
Let R be a unique factorization domain and let a be non zero element of R with a=p_1^(α1)p_2^(α2)...P_n^(αn ), where pi are prime elements and αi are positive integers. Show that the number of divisors of a is the product of (1+αi ) where i=1,2,...,n
May be we can proceed by induction, but how can we start.
Thank you in advance