Prime Divisors
Prove that
\[
p\nmid n.
\]
Suppose $n$ has prime factorization
\[
n=p_1^{a_1}p_2^{a_2}\cdots p_r^{a_r},
\]
and $p$ is a prime such that
\[
p\notin\{p_1,p_2,\ldots,p_r\}.
\]
Prove that
\[
p\nmid n.
\]
Suppose $n$ has prime factorization
\[
n=p_1^{a_1}p_2^{a_2}\cdots p_r^{a_r},
\]
and $p$ is a prime such that
\[
p\notin\{p_1,p_2,\ldots,p_r\}.
\]