# Show that $\mathbb Z$ is generated by 5 and 7

So I am in week 3 of my intro to group theory class, and I'm lost! My teacher did not go over generators of groups in class. The book is not much help to me either. Any help getting this started would be great!

Show that $\mathbb Z$ is generated by 5 and 7

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Show that every $n \in \mathbb{Z}$ can be written as $n=5m+7k$ with $m,k \in \mathbb{Z}$. –  njguliyev Oct 15 '13 at 21:09
Do you know what is meant by "$5$ and $7$ generates $\mathbb{Z}$"? Can you given an English translation of what you think that means? –  EuYu Oct 15 '13 at 21:10

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