Given a prime p and an integer n , let (n) denote the largest integer k such that p^k divides n . Define f(n)=p^ - (n) . Then

Options

1. Af (p^r ) f (p^s ) if r s
2. Bf(m) f(n) if m divides n .
3. Cf(n m)=f(n) f(m) for all n, m N .
4. Df(n+m)=p^ (- (n),- (m)) for all n, m N , where (- (n),- (m)) is the maximum of - (n) and - (m) .