nwessel nwessel

14-03-2017
Mathematics

Answered

Show that if a ≡ b (mod n) and m divides n, then a ≡ b (mod m).

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LammettHash LammettHash

15-03-2017

If \(a\equiv b\mod n\), then there is some integer \(N\) such that \(a=Nn+b\). Because \(m|n\), it follows that \(m|Nn\), which means there is some integer \(M\) such that \(a=Mm+b\), which is equivalent to the statement that \(a\equiv b\mod m\).

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