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

$m, n, \in N; d i s t h e g r e a t e s t$ $c o m m o n d i v i s o r o f m a n d n .$ $w e s u p p o s e m = {d m}^{'} a n d n = {d n}^{'}$ $w i t h m^{'} a n d n^{'} \in N .$ $s h o w t h a t \exists u, v \in Z s u c h$ $t h a t m u - n v = d$
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