Re: proof
On 1 May 2007 16:12:38 -0700, edpdpub@xxxxxxxxxxx wrote:
Let a,b, and n be integers with n>0, prove that if a = b (mod n) and
(a,n) = 1, then (b,n)=1.
= means congruent
can anyone prove this, i am having lots of troubles
thanks!
Given a,b,n integers with n>0, a=b mod n, and (a,n)=1.
Suppose (b,n)>1.
It follows that b and n must have a common factor d, where d>1.
Then a=b mod n => n | (a-b) => d | (a-b) => d | ((a-b) + b) => d | a
contrary to the assumption that (a,n)=1.
Therefore (b,n)=1.
quasi
.
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