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Category: Number Theory

1-a-m-b-m-1-ab-m-1-2-c-ab-and-c-a-1-c-b-3-If-c-is-a-common-multiple-of-a-and-b-then-a-b-c-4-ma-mb-m-a-b-for-all-int-m-gt-0-5-a-b-a-b-ab-6-Let-g-gt-0-s-be-integers-Sh

Question Number 124944 by udaythool last updated on 07/Dec/20 1.(a,m)=(b,m)=1(ab,m)=12.caband(c,a)=1cb3.Ifcisacommonmultipleofaandbthen[a,b]c4.[ma,mb]=m[a,b]forallintm>05.[a,b](a,b)=∣ab6.Letg>0,sbeintegers.Show$$\mathrm{that}\:{g}\mid{s}\:\mathrm{iff}\:\exists\:\mathrm{integers}\:{x},\:{y}\:\mathrm{such} \