.a*2, a*3, ldots

divides

This is what $a$ divides $b$ means. The shorthand notation is$$a|b$$.

In your example, $$a|a^2\iff a\leq a^2$$since by definition there exists $c$ such that $a^2 = ac$, namely $a = c$.

integer

Alternatively, you might want to remember this phrase: "$2$ divides $6$ into $3$ parts" to remember what "$2$ divides $6$" means.This would explain $2 dividing 6$.

Note that $2 | 0$ because $0$ is an integer multiple of $2$: $0 = k2$ for some integer $k$. Just take $k=0$.

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