How do I get from $3 + 6 x$ is congruent to $0$ modulo $9$ to the statement $1 + 2 x$ is congruent to $0$ modulo $3$? What is the reason that I can just "divide everything by $3$"?
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3Consider $3+6x=9k$ for some integer $k$, by the definition of modulo $0$ mod $9$. What do you get when you divide both sides by $3$? – dgeyfman Sep 04 '23 at 16:26