5
votes
0answers
109 views

On the ratio of Gilbreath sequences

Definitions: let $n \in \mathbb{N}_{>0} \cup \{ \infty \}$ and let $E_n$ be the set of sequences $(d_i)_{i=1}^n$ such that $d_1=1$, $d_i$ is an even integer (for $i > 1$) and $0<d_i \le i$. ...
19
votes
1answer
515 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 ...
33
votes
2answers
2k 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 ...
22
votes
1answer
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
1answer
544 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
3answers
603 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
2answers
463 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
1answer
467 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
1answer
650 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
1answer
344 views

Can we count primes in residue classes quickly?

Using combinatorial methods (due to Legendre, Lehmer, Meissel, Lagarias, Miller, Odlyzko, Del├ęglise, Rivat, and probably others) it's possible to count the number of primes up to $N$ quickly -- in ...
8
votes
3answers
824 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 ...
10
votes
6answers
15k 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
3answers
343 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 ...