I am guessing the following statement is true:
For two integers $a$ and $b$ greater than $1$, $(a,b)=1$ if and only if $a$ does not divide $b$ and $b$ does not divide $a$.
Could anyone please confirm? Also if this statement is true, is it in the most general form relating the condition $(a,b)=1$ to non-divisibility of $a$ and $b$? In other words, is it true $a$ and $b$ must be integers greater than $1$?