Results 1 to 10 of about 35 (35)
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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Veterinary Dermatology, Volume 34, Issue 6, Page 489-494, December 2023., 2023 Background – Dilute sodium hypochlorite (bleach) baths at 0.005% concentration twice weekly have been shown to markedly reduce the severity of atopic dermatitis in children, yet no tolerability and efficacy data are available for this treatment in dogs.
Frane Banovic +4 more
wiley +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
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, 2010 11 páginas.-- 2010 Mathematics subject classification: Primary 11N25; Secondary 11B39.A Lehmer number is a composite positive integer n such that ϕ(n)|n − 1.
Cilleruelo, Javier +3 more
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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 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
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
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On the distribution of powered numbers
Open MathematicsAsymptotic 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
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On the ratio of the sum of divisors and Euler’s totient function II [PDF]
, 2014 We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the quotient is 4 and n is ...
Qizhi Zhou +3 more
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