# Tagged Questions

**2**

votes

**1**answer

539 views

### A formula combining Euler $\phi$ and $\gcd$

Let us fix a natural number $N>1$ and $a_1, \ldots, a_n$ natural numbers satisfying $0 \leq a_i < N$, with the property that $1+ \sum a_i$ is divisible by $N$. Let $\phi$ be the Euler totient ...

**4**

votes

**0**answers

283 views

### Generalization of Tamarkinâ€™s ARO 1993, final round, problem 10/8: part II

Let us use the notations of my previous question about Tamarkin's problem.
Let $\ell\in\left\lbrace 0,1,...,p\right\rbrace$.
An element $f\in \mathbb Z^{\mathbb Z}$ is said to be ...

**29**

votes

**2**answers

2k views

### Generalization of Tamarkin's ARO 1993, final round, problem 10/8: still a conjecture?

This is from the category "problems I cannot believe that are still open". But then again, I don't know whether it is still open; it seems to have escaped the attention of most number theorists and ...

**17**

votes

**3**answers

1k views

### A binomial sum is divisible by p^2

This is a question I have since longer time, but I have absolutely no idea how to proceed on it.
Let $p>3$ be a prime. Prove that ...