Claim:Bézout coefficients exist

Claim (see proof):

For all [math]a, b \href{/cs2800/wiki/index.php/%E2%88%88}{∈} \href{/cs2800/wiki/index.php/%E2%84%95}{ℕ} [/math], there exists [math]s, t \href{/cs2800/wiki/index.php/%E2%88%88}{∈} \href{/cs2800/wiki/index.php/%E2%84%A4}{ℤ} [/math] such that [math]\href{/cs2800/wiki/index.php/Gcd}{gcd}(a,b) = sa + tb [/math].

[math]s [/math] and [math]t [/math] satisfying this equation are called Bézout coefficients of [math]a [/math] and [math]b [/math].