If $a \gt 1$ and if $a$ has the property that whenever $a|bc$ then $a|b$ or $a|c$, show that $a$ must be a prime.
Not sure how tot prove this, so I started out by checking a few values..
$2|7*4$, where $2 \nmid 7$ but $2|4$ so this $a=2=$prime checks out.
$3|7*6$, where $3 \nmid 7$ but $3|6$ so this $a=3=$prime checks out.
$5|7*15$, where $5 \nmid 7$ but $5|15$ so this $a=5=$prime checks out.
What about not a prime?
$6|4*3$, where $6 \nmid 4$ and $6 \nmid 3$ so $a$ must be a prime
Before, everyone freaks out that "proof by example, isn't a proof"... I know. This is all I could manage. I find writing proofs to be difficult.