Question 20
Let $k \ge 1$, be a positive integer, let $p_1, p_2, \dots, p_k$ be distinct primes and denote $n = p_1p_2\dots p_k$. For a function $f : \{1, 2, \dots, n\} \to \{1, 2, \dots, n\}$, define $p(f) = f(1)f(2)\dots f(n)$.
a) Determine the number of functions $f$ such that $p(f)$ divides $n$.
b) For $n=6$, determine the number of functions $f$ such that $p(f)$ divides $36$.
a) Determine the number of functions $f$ such that $p(f)$ divides $n$.
b) For $n=6$, determine the number of functions $f$ such that $p(f)$ divides $36$.