Results 1 to 10 of about 350 (60)
On Types of Elliptic Pseudoprimes [PDF]
Groups, Complexity, Cryptology, 2021 We generalize the notions of elliptic pseudoprimes and elliptic Carmichael numbers introduced by Silverman to analogues of Euler-Jacobi and strong pseudoprimes.
L. Babinkostova +2 more
doaj +1 more source
Squarefree Integers in Arithmetic Progressions to Smooth Moduli
Forum of Mathematics, Sigma, 2021 Let $\varepsilon> 0$ be sufficiently small and let $0 < \eta < 1/522$ . We show that if X is large enough in terms of $\varepsilon $ , then for any squarefree integer $q \leq X^{196/261-\varepsilon }$ that is $X^{\eta ...
Alexander P. Mangerel
doaj +1 more source
AN AVERAGE THEOREM FOR TUPLES OF k‐FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Mathematika, Volume 67, Issue 1, Page 1-35, January 2021., 2021 Abstract In the spirit of the Hooley–Montgomery refinement of the Barban–Davenport‐Halberstam theorem, we obtain an asymptotic formula for the variance associated with tuples of k‐free numbers in arithmetic progressions.
Tomos Parry
wiley +1 more source
Piatetski-Shapiro sequences [PDF]
, 2012 We consider various arithmetic questions for the Piatetski-Shapiro sequences bncc (n = 1, 2, 3, . . .) with c > 1, c 6∈ N. We exhibit a positive function θ(c) with the property that the largest prime factor of bncc exceeds nθ(c)−e infinitely often. For c
R. Baker +4 more
semanticscholar +1 more source
Small gaps between products of two primes [PDF]
, 2006 Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $$\liminf_{n\to \infty} (q_{n+1}-q_n) \le 6.$$ This sharpens an earlier result of the authors (arXivMath NT/0506067), which had 26 in place of 6 ...
Goldston, D. A. +3 more
core +3 more sources
SIGN PATTERNS OF THE LIOUVILLE AND MÖBIUS FUNCTIONS
Forum of Mathematics, Sigma, 2016 Let ${\it\lambda}$ and ${\it\mu}$ denote the Liouville and
KAISA MATOMÄKI +2 more
doaj +1 more source
On the greatest common divisor of $n$ and the $n$th Fibonacci number [PDF]
, 2017 Let $\mathcal{A}$ be the set of all integers of the form $\gcd(n, F_n)$, where $n$ is a positive integer and $F_n$ denotes the $n$th Fibonacci number.
Leonetti, Paolo, Sanna, Carlo
core +2 more sources
The density of numbers $n$ having a prescribed G.C.D. with the $n$th Fibonacci number [PDF]
, 2018 For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number.
Sanna, Carlo, Tron, Emanuele
core +5 more sources
Sums and differences of power-free numbers [PDF]
, 2015 We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions $a, b \in \mathbb N$ to the equations $a+b=n$ and $a-b=n$, where $a$ is $k$-free and $b$ is $l$-free.
Brandes, Julia
core +1 more source
On a thin set of integers involving the largest prime factor function
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 19, Page 1185-1192, 2003., 2003 For each integer n ≥ 2, let P(n) denote its largest prime factor. Let S : = {n ≥ 2 : n does not divide P(n)!} and S(x) : = #{n ≤ x : n ∈ S}. Erdős (1991) conjectured that S is a set of zero density. This was proved by Kastanas (1994) who established that S(x) = O(x/logx). Recently, Akbik (1999) proved that S(x)=O(x exp{−(14/)logx}).
Jean-Marie De Koninck, Nicolas Doyon
wiley +1 more source