Q. If $a_1,a_2,a_3 ......a_n+1 $ be $ ( n + 1 ) $ different prime numbers, then the number of different factors (other than $1$) of a number of the the form $ N = a_1^m a_2a_3.....a_{n+1})$,
1) $m +1$
2) $ (m+1)2^n$
3) $m.2^n + 1 $
4) None of these
Only one option is correct
I thought , I can chose $a_1$ in $(m+1)$ ways being alike and others can be selected in $(1+1)........n$ times $= 2^n$) hence using multiplication principle option 2nd will be correct but that is wrong and I do not why it is wrong. The answer is 4th option. There is no explanation of answer in the book. Please tell me then what will be the answer.