# 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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### when is $\frac{1}{n}\binom{n}{r}$ an integer

So I am considering for which values of n is $a_n =\frac{1}{n}\binom{n}{r}$ an integer for all $1\leq r \leq n-1$. The first thing I did was to check the Pascal Triangle. So I guess n has to be ...
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### 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 ...
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### Using Newton Raphsons method

Apply Newtons Method to the function $f(x)= a-\frac{1}{x}$ to compute $\frac{1}{a}$ for positive $a$. Answer can't have any division in it but can include addition, subtraction and multiplication. ...
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### My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

What do you think about my first proof that uses the well-ordering principle? Please mark/grade. Theorem The sum of the cubes of three consecutive natural numbers is a multiple of 9. Proof First,...
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### Q: Prove: $gcd(a,n)=1, n \in \mathbb{N}, a \in \mathbb{Z} \implies \forall c \in \mathbb{Z}\ \exists m \in \mathbb{Z}\,:\, ma=c \pmod{n}$

I was trying to prove the next simple statement ,without success thus far. Suppose that $gcd(a,n)=1$, where $n \in \mathbb{N}$ and $a \in \mathbb{Z}$. Show that for all $c \in \mathbb{Z}$ there ...