### Playing With Numbers

goals
Prove that if $a$ is an integer, then ${a^3} - a$ is divisible by $6$.Also deduce that $5{a^3} + 13a - 30$ is divisible by 6.
A, CD, GHI, .... UVWXY
If $k$ is any even positive integer, then $(k^{2} + 2k)$ is
$50B$ is a number divisible by $5$, what might be the value of $B$?
Check whether $6582$ is divisible by $4$?