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

User Paul Wang
by
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1 Answer

5 votes
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.
User Fcs
by
8.1k points
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