Daniel J Smith Custom TMUA alpha · Question 3

We say an integer $x$ divides an integer $y$ and write $x\mid y$ if there exists an integer $k$ such that $y=kx$

Let $a,b,n$ be positive integers. Let $(*)$ the statement

(*)\quad n\mid ab

Let C be the statement:

For every prime $p$ with $p\mid n$ , either $p\mid a$ or $p\mid b$

This condition $C$ is:

Anecessary but not sufficient for

(*)

Bsufficient but not necessary for

(*)

Cnecessary and sufficient for

(*)

Dneither necessary nor sufficient for

(*)

examday