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### I only don't understand one line in this given proof regarding a sequence becoming constant modulo n

It is strong induction on $n$. The author is saying: Assume by strong induction that $$x_{k}\equiv x_{k+1}\ (\text{mod }m)$$ for all $k\geq m$ and all $m<n$. The author is doing induction on $n$, ...
• 11.1k
1 vote

### Name for integer "quotient" rounded up (ceiling) instead of down (floor), and its negative or complementary "remainder"

This isn't intended as a complete and definitive answer, more a list of places I've seen this concept crop up and writers have seen fit to give it a name. Aside from elementary number theory, careful ...
• 1,347

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