Results 1 to 10 of about 312 (25)
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
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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
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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
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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
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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
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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
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
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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
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, 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.
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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.
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