Coprime


Definition 1

Two integers are coprime if and only if the only integer that divides both of them is \(1\).

Definition 2

$$\forall a,b \in \mathbb{Z} : a \perp b \Leftrightarrow gcd(a, b) = 1$$
THEOREM    $$\forall a \in \mathbb{Z} : 1 \perp a$$
coprime_1_left: coprime 1 ?a

Proof unavailable

THEOREM    $$\forall a \in \mathbb{Z} : a \perp 1$$
coprime_1_left: coprime 1 ?a

Proof unavailable

THEOREM   

The coprimality relation is not transitive.

Proof available

THEOREM   

The coprimality relation is not antitransitive.

Proof available

THEOREM   

The coprimality relation is non-transitive.

Proof available

See also

Properties of coprime integers - Wikipedia

Parent topics