Polynomial ring/Field/Lemma of Bezout/Coprime/Fact

Let ${}K$ be a field and let ${}P_{1},\ldots ,P_{n}$ denote coprime polynomials over ${}K$.

Then there exists a representation

${}Q_{1}P_{1}+\cdots +Q_{n}P_{n}=1\,$

with

${}Q_{1},\ldots ,Q_{n}\in K[X]$.

Proof, Write another proof