Results 11 to 20 of about 350 (60)

Distribution of integral values for the ratio of two linear recurrences [PDF]

, 2017
Let $F$ and $G$ be linear recurrences over a number field $\mathbb{K}$, and let $\mathfrak{R}$ be a finitely generated subring of $\mathbb{K}$. Furthermore, let $\mathcal{N}$ be the set of positive integers $n$ such that $G(n) \neq 0$ and $F(n) / G(n ...
Sanna, Carlo
core   +3 more sources

On a density problem of Erdös

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 655-658, 1999., 1999
For a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x) = 𝒮 = {n ≤ x : n does not divide P(n)!}. Paul Erdös has proposed that |S| = o(x) as x → ∞, where |S| is the number of n ∈ S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that .
Safwan Akbik
wiley   +1 more source

On the maximal and minimal exponent of the prime power divisors of integers

Publicationes mathematicae (Debrecen), 2006
For some integer n and prime p let νp(n) be the largest nonnegative integer for which pp is a divisor of n. Let h(n) = minp|n νp(n), H(n) = maxp|n νp(n). The mean value of h, H over some subsets of integers is investigated. 1. Let P be the set of primes,
Subbarao Edmonton, M. Subbarao
semanticscholar   +1 more source

Restricted divisor sums [PDF]

, 2002
There is a body of work in the literature on various restricted sums of the number of divisors of an integer function including that described in [2-9, 11] and summarised in Section 2 ...
Broughan, Kevin A.
core   +2 more sources

Big Biases Amongst Products of Two Primes [PDF]

, 2016
We show that substantially more than a quarter of the odd integers of the form pqpq up to xx, with p,qp,q both prime, satisfy p≡q≡3 (mod4)p≡q≡3 (mod4)
Dummit, D, Granville, A, Kisilevsky, H
core   +2 more sources

Approximation by Several Rationals

, 2007
Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a_1/q_1, ..., a_n/q_n with smaller denominators. We show that in the special cases of n=3 and n=4 and certain admissible
Shparlinski, Igor E.
core   +1 more source

On curves over finite fields with Jacobians of small exponent

, 2008
We show that finite fields over which there is a curve of a given genus g with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the case g=1.
Ford, Kevin, Shparlinski, Igor
core   +1 more source

It is easy to determine whether a given integer is prime

, 2004
“The problem of distinguishing prime numbers from composite numbers, and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
A. Granville
semanticscholar   +1 more source

On the distribution of powered numbers

Open Mathematics
Asymptotic formulae are established for the number of natural numbers mm with largest square-free divisor not exceeding mϑ{m}^{{\vartheta }}, for any fixed positive parameter ϑ{\vartheta }. Related counting functions are also considered.
Brüdern Jörg, Robert Olivier
doaj   +1 more source

The density of twins of $k$-free numbers

, 2014
For $k \geq 2$, we consider the number $A_k(Z)$ of positive integers $n \leq Z$ such that both $n$ and $n+1$ are $k$-free. We prove an asymptotic formula $A_k(Z) = c_k Z + O(Z^{14/(9k)+\epsilon})$, where the error term improves upon previously known ...
Dietmann, Rainer, Marmon, Oscar
core   +1 more source