(1) (4 pts) Prove that if $a, b, c$ and $d$ are integers, where $a eq 0$, such that $a \mid c$ and $b \mid d$, then $a b \mid c d$. (2) (4 pts) Prove that if $a$ is a positive integer then 4 does not divide $a^{2}+2$. CS.PB.003 (1) (4 pts) Prove that if $a, b, c$ and $d$ are integers, where $a eq 0$, such that $a \mid c$ and $b \mid d$, then $a b \mid c d$. (2) (4 pts) Prove that if $a$ is a positive integer then 4 does not divide $a^{2}+2$. CS.PB.003