# Tagged Questions

This tag is for questions about divisibility, that is, determining when one thing is a multiple of another thing.

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### Proof by contrapositive: $4 \nmid (n-2)^2 \implies 6 \nmid n$

Prove: $4 \nmid (n-2)^2 \implies 6 \nmid n$ Proof by contrapositive: $6 \mid n \implies 4 \mid (n-2)^2$ $n=6k,$ $k \in \mathbb Z$ $((6k)-2)^2 = 36k^2 - 24k+4 = 4(9k^2 - 6k+1), (n-2)^2=4c$ ...
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### Sow divisibility with congruence equation

I have this math question that I'm kind of stuck on. Suppose that the congruence equation $ax \equiv b \pmod{n}$ has at least one solution. Let $d = \gcd{(a, n)}$. Show that $d \mid b$. I ...
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### When $\frac{1}{n}\binom{n}{r}$ is an integer , again?
This question follows a previous one If $n$ and $r$ are coprime then $a_{n,r}=\frac{1}{n}\binom{n}{r}$ is integer but this is not a necessary condition. Question: what is a necessary and ...
### How many sequences of the form $1a_1a_2…a_n1$ have each $a_i$ dividing the sum of its two neighbors?
For each $n \in \mathbb{N}$, how many sequences of the form $1a_1a_2...a_n1$ with the $a_i \in \mathbb{N}$ have each $a_i$ dividing the sum of its two neighbors? I just came across this, and ...