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 $$2 \perp 3, 3 \perp 5, 2 \perp 5$$.