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show-that-a-b-N-if-GCD-a-b-then-Z-au-bv-u-and-v-Z-




Question Number 124690 by mathocean1 last updated on 05/Dec/20
show that ∀ a,b∈N^∗  if δ=GCD(a;b)   then δZ={au+bv; u and v ∈Z}
$${show}\:{that}\:\forall\:{a},{b}\in\mathbb{N}^{\ast} \:{if}\:\delta={GCD}\left({a};{b}\right)\: \\ $$$${then}\:\delta\mathbb{Z}=\left\{{au}+{bv};\:{u}\:{and}\:{v}\:\in\mathbb{Z}\right\} \\ $$

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