(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to prove the following claim.

Claim: For any positive integers m and n, m and n both greater than 1, if n|m and a≡b(mod m), then a≡b(mod n).

2. Relevant equations

n/a

3. The attempt at a solution

so i first changed each equation (ex: a≡b(mod m)) to a=b+qm and a=b+qn

I figured in these forms I could show that the equations are equal.

so I eventually get (a-b)/q=m or =n respectively. So I believe this shows their equality, but i am completely unsure because it won't always work I don't think. I need to also show that n|m. So tired dividing the m=(a-b)/q by the n= equation and of course I just get 1...

To be completely honest I am not quite sure how to prove this. I am not quite familiar with the mod function and I am incredibly weak with proofs. If anyone can give me insight into solving this problem I would great appreciative.

also note that this should be able to be done with a direct proof.

thanks!

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# Discrete Math - a modulus proof

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