So given a set \$S = a, a^2, a^3, ldots\$, with relation \$a | b leftrightarrow a leq b\$, does the relation hold going from left to right or right to left? i.e. \$a|a^2, a^2|a^3,ldots\$  \$egingroup\$ Let \$(G,circ)\$ be a group. We then say that \$amid b\$ (read as "\$a\$ divides \$b\$") if, \$\$exists cin Gmid b=acirc c\$\$ \$endgroup\$
Given two integers \$a\$ and \$b\$, we say \$a\$ divides \$b\$ if there is an integer \$c\$ such that \$b=ac\$. Source.

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

In your example, \$\$a|a^2iff aleq a^2\$\$since by definition there exists \$c\$ such that \$a^2 = ac\$, namely \$a = c\$. We say \$a\$ divides \$b\$, denoted by \$a | b\$, if \$b\$ is a multiple of \$a\$ (ie, \$b\$ is an integer multiple of \$a\$). Equivalently, \$a |b\$ iff \$b=ka\$ for some integer \$k\$.

To remember what "\$2\$ divides \$6\$" means, perhaps you can remember the phrase "\$2\$ divides \$6\$ into \$3\$ parts". Hence, \$2 | 6\$.

Note that \$2 | 0\$ because \$0\$ is an integer multiple of \$2\$: \$0 = k2\$ for some integer \$k\$. Just take \$k=0\$. Thanks for contributing an answer to chathamtownfc.netematics Stack Exchange!

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