Averaged forms of two conjectures of Erdős and Pomerance, and their applications
Y Jiang, G Lü, Z Wang - Advances in Mathematics, 2022 - Elsevier
Let P+(n) denote the largest prime factor of an integer n. In this paper, we study the
asymptotics of sums∑ p⩽ x P+(p+ h)⩽ y 1 and∑ n⩽ x, P+(n)⩽ y 1 P+(n+ h)⩽ y 2 1 for x ε⩽ y …
asymptotics of sums∑ p⩽ x P+(p+ h)⩽ y 1 and∑ n⩽ x, P+(n)⩽ y 1 P+(n+ h)⩽ y 2 1 for x ε⩽ y …
Prime chains and Pratt trees
K Ford, SV Konyagin, F Luca - Geometric and Functional Analysis, 2010 - Springer
Prime chains are sequences p_ 1, ..., p_ k of primes for which p_ j+ 1 ≡ 1 (mod pj) for each j.
We introduce three new methods for counting long prime chains. The first is used to show …
We introduce three new methods for counting long prime chains. The first is used to show …
Ramanujan-style congruences for prime level
We establish Ramanujan-style congruences modulo certain primes ℓ between an Eisenstein
series of weight k, prime level p and a cuspidal newform in the ε-eigenspace of the Atkin …
series of weight k, prime level p and a cuspidal newform in the ε-eigenspace of the Atkin …
On the iterates of the shifted Euler's function
P Leonetti, F Luca - Bulletin of the Australian Mathematical Society, 2024 - cambridge.org
Abstract Let $\varphi $ be Euler's function and fix an integer $ k\ge 0$. We show that for
every initial value $ x_1\ge 1$, the sequence of positive integers $(x_n) _ {n\ge 1} $ defined …
every initial value $ x_1\ge 1$, the sequence of positive integers $(x_n) _ {n\ge 1} $ defined …
The number of preimages of iterates of ϕ and σ
A Akande - Journal of Number Theory, 2024 - Elsevier
Abstract Paul Erdos and Carl Pomerance have proofs on an asymptotic upper bound on the
number of preimages of Euler's totient function ϕ and the sum-of-divisors functions σ. In this …
number of preimages of Euler's totient function ϕ and the sum-of-divisors functions σ. In this …
On amicable numbers
C Pomerance - Analytic Number Theory: In Honor of Helmut Maier's …, 2015 - Springer
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Account Menu Find a journal Publish with us Track your research Search Cart Book cover …
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On the Equation ax ≡ x (mod b)
J Germain - 2009 - degruyter.com
Abstract Recently Jiménez-Urroz and Yebra [On the Equation ax≡ x (mod bn)] constructed,
for any given a and b, solutions x to the title equation. Moreover they showed how these can …
for any given a and b, solutions x to the title equation. Moreover they showed how these can …
The reciprocal sum of divisors of Mersenne numbers
Z Engberg, P Pollack - arXiv preprint arXiv:2006.02373, 2020 - arxiv.org
We investigate various questions concerning the reciprocal sum of divisors, or prime
divisors, of the Mersenne numbers $2^ n-1$. Conditional on the Elliott-Halberstam …
divisors, of the Mersenne numbers $2^ n-1$. Conditional on the Elliott-Halberstam …
Divisibility, smoothness and cryptographic applications
D Naccache, IE Shparlinski - Algebraic Aspects of Digital …, 2009 - ebooks.iospress.nl
Divisibility, Smoothness and Cryptographic Applications Page 1 Divisibility, Smoothness and
Cryptographic Applications David Naccache a, Igor E. Shparlinski b a Equipe de cryptographie …
Cryptographic Applications David Naccache a, Igor E. Shparlinski b a Equipe de cryptographie …
Counting integers with a smooth totient
WD Banks, JB Friedlander, C Pomerance… - … Quarterly Journal of …, 2019 - academic.oup.com
COUNTING INTEGERS WITH A SMOOTH TOTIENT | The Quarterly Journal of Mathematics |
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