1. Recall the following theorem. Theorem 1. Let a, b, m,n e N, m, n >...

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1. Recall the following theorem. Theorem 1. Let a, b, m,n e N, m, n > 0 and ged(m,n) = 1. There erists a unique r e Zmn such

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Answer 1

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Suppose that there are two solutions Ꮖ . of the system. That is,

ш рош h =D=0
u pour f =9=2 .

By subtracting we get that I h satisfies

250 mod m
(u pour 0=2

so that m| z and . Since ged(n,m) = 1 we conclude that mn 2 . That is, (иш рош 0 = 2 . Recalling the definition of we have иш рош pou) 0 =h - or (иш рош) К = as we wanterd.

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