m-n-N-d-is-the-greatest-common-divisor-of-m-and-n-we-suppose-m-dm-and-n-dn-with-m-and-n-N-show-that-u-v-Z-such-that-mu-nv-d-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 127540 by mathocean1 last updated on 30/Dec/20

m, n, ∈ N ; d is the greatest common divisor of m and n. we suppose m=dm′ and n=dn′ with m′ and n′ ∈ N. show that ∃ u,v ∈ Z such that mu−nv=d

$${m},\:{n},\:\in\:\mathbb{N}\:;\:{d}\:{is}\:{the}\:{greatest} \\ $$$${common}\:{divisor}\:{of}\:{m}\:{and}\:{n}.\: \\ $$$${we}\:{suppose}\:{m}={dm}'\:{and}\:{n}={dn}'\: \\ $$$${with}\:{m}'\:{and}\:{n}'\:\in\:\mathbb{N}. \\ $$$${show}\:{that}\:\exists\:{u},{v}\:\in\:\mathbb{Z}\:{such}\: \\ $$$${that}\:{mu}−{nv}={d} \\ $$

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m-n-N-d-is-the-greatest-common-divisor-of-m-and-n-we-suppose-m-dm-and-n-dn-with-m-and-n-N-show-that-u-v-Z-such-that-mu-nv-d-

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