Definition:Coprime

Definition
Let $a$ and $b$ be integers such that $b \ne 0$ and $a \ne 0$ (i.e. they are not both zero).

Let $\gcd \left\{{a, b}\right\}$ be the greatest common divisor of $a$ and $b$.

If $\gcd \left\{{a, b}\right\} = 1$, then $a$ and $b$ are coprime, or relatively prime.

Alternatively we can say $a$ is prime to $b$.

If $\gcd \left\{{a, b}\right\} = 1$, then the notation $a \perp b$ is encouraged.

If $\gcd \left\{{a, b}\right\} \ne 1$, the notation $a \not \perp b$ can be used.

It can be seen that considered as a relation, $\perp$ is:


 * 1) Non-reflexive: $a \not \perp a$ except when $a = \pm 1$
 * 2) Symmetric: $a \perp b \iff b \perp a$
 * 3) Not antisymmetric: $a \perp b \land b \perp a \not \implies a = b$
 * 4) Non-transitive: Consider $2 \perp 3, 3 \perp 4, 2 \not \perp 4$ and $2 \perp 3, 3 \perp 5, 2 \perp 5$.