# Tagged Questions

**19**

votes

**1**answer

494 views

### Avoiding multiples of $p$

Let $p$ be a prime number and $P=\{1,2,...,p-1\}$
In how many ways we can sum all the elements of $P$ in such a way that we will reach a multiple of $p$
only when we sum the last summand?
For ...

**30**

votes

**2**answers

1k views

### A question on maps from $\mathbb{Z}/p\mathbb{Z}$ to itself

Let $p\geq 3$ be a prime number, and let $u:\mathbb{Z}/p\mathbb{Z}\to \mathbb{Z}/p\mathbb{Z}$ be a map such that, for all $l\in \mathbb{Z}/p\mathbb{Z}$,$l\neq 0$, the map $k\mapsto u(k+l)-u(k)$ is a ...

**18**

votes

**0**answers

1k views

### Permutations of $(Z/pZ)^*$

Let $p$ be a prime integer, and let $(\mathbb Z/p\mathbb Z)^*$ be the set of non-zero elements of $\mathbb Z/p \mathbb Z$.
Denote by $S((\mathbb Z/p \mathbb Z)^*)$ the group of permutations of ...

**2**

votes

**1**answer

531 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

**3**answers

589 views

### Mathematical techniques to reduce the amount of storage memory

Apologies for the length question. Those acquainted with the analytics industry will know that the next big thing in the information technology world will be the Big Data revolution where huge volumes ...

**0**

votes

**2**answers

425 views

### primes dividing binomial coefficients

Dear All,
I am considering maximal subgroups of odd index in Alternating and Symmetric groups, and this leeds me to some questions on binomial coefficients that I presently do not know and that I ...

**6**

votes

**1**answer

463 views

### Given an odd integer N find the smalletst prime p > N such that (p-1,N)=1

So the title says it all,
>
Q: Given a large odd integer $N>>0$, what can we prove about the smallest prime
$p>N$ such that $gcd(p-1,N)=1$?
Note that such a prime exists: Given an ...

**7**

votes

**1**answer

649 views

### looking for a multiplicity one prime in a finite sum

So I'm trying to compute the Galois group of family of polynomials (indexed by their degree) using the technique of the Newton polygon. In order to apply this technique I need to find some good prime ...

**4**

votes

**1**answer

331 views

### Can we count primes in residue classes quickly?

Using combinatorial methods (due to Legendre, Lehmer, Meissel, Lagarias, Miller, Odlyzko, Deléglise, Rivat, and probably others) it's possible to count the number of primes up to $N$ quickly -- in ...

**8**

votes

**3**answers

822 views

### Boolean Cube of Primes

For a large enough $n$, and a parameter $ m $ I'm looking for a subset of the prime numbers in the range $[n,2n]$ with a unique structure. I am looking for a prime $p$ and a set of $m$ positive (not ...

**9**

votes

**6**answers

14k views

### Pascal Triangle and Prime Numbers

My question @ StackOverflow just got closed as not programing related so I'm posting here.
Please refer to the question @ SO, since:
sorry, new users can only post a maximum of one hyperlink
sorry, ...

**6**

votes

**3**answers

340 views

### Prime numbers and strings of symbols

Suppose you have N symbols (e.g. "1","2",...,"N" or "a","b",...,"$") and a string of these symbols (say, the first trillion digits of pi). Then does there exist a prime number whose N-ary ...