Results 1 to 10 of about 19,257 (101)
Indagationes Mathematicae, 2021 In part I of this paper we studied additive decomposability of the set $\F_y$ of th $y$-smooth numbers and the multiplicative decomposability of the shifted set $\g_y=\F_y+\{1\}$. In this paper, focusing on the case of 'large' functions $y$, we continue the study of these problems. Further, we also investigate a problem related to the m-decomposability
Győry, K., Hajdu, L., Sárközy, A.
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On some links between the generalised Lucas pseudoprimes of level k
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences.
Andrica Dorin +2 more
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The Bombieri-Vinogradov theorem for nilsequences
Discrete Analysis, 2021 The Bombieri-Vinogradov theorem for nilsequences, Discrete Analysis 2021:21, 55 pp. The prime number theorem asserts that the density of the primes in the vicinity of a large integer $n$ is approximately $1/\log n$, or equivalently that the number of ...
Xuancheng Shao, Joni Teräväinen
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Perwira Journal of Science & Engineering, 2022 . A Catalan number is a positive number obtained by calculating the combined structure of a sequence. Catalan numbers have a general form and a recursive form that can be identified through Diagonal-Avoiding Paths and Balanced Parentheses. Catalan numbers have congruence on the modulo of integers. One of them is on the prime number modulo p. For every
Agus Sugandha, null Irfan Azkamahendra
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A decomposition of multicorrelation sequences for commuting transformations along primes
Discrete Analysis, 2021 A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer $k$ and every $\delta>0$ there exists $n$ such that every subset of $\
Anh N. Le, Joel Moreira, Florian Richter
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On a conjecture of Gowers and Wolf
Discrete Analysis, 2022 On a conjecture of Gowers and Wolf, Discrete Analysis 2022:10, 13 pp. Szemerédi's theorem asserts that for every $\delta>0$ and every positive integer $k$ there exists $n$ such that every subset $A$ of $\{1,2,\dots,n\}$ of size at least $\delta n ...
Daniel Altman
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On General Prime Number Theorems with Remainder [PDF]
, 2017 We show that for Beurling generalized numbers the prime number theorem in remainder form $$\pi(x) = \operatorname*{Li}(x) + O\left(\frac{x}{\log^{n}x}\right) \quad \mbox{for all } n\in\mathbb{N}$$ is equivalent to (for some $a>0$) $$N(x) = ax + O\left ...
Debruyne, Gregory, Vindas, Jasson
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Fast integer multiplication using generalized Fermat primes [PDF]
, 2018 For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n $\times$ log n $\times$ log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer proved that there exists
Covanov, Svyatoslav, Thomé, Emmanuel
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POLYNOMIAL PATTERNS IN THE PRIMES
Forum of Mathematics, Pi, 2018 Let $P_{1},\ldots ,P_{k}:\mathbb{Z}\rightarrow \mathbb{Z}$ be polynomials of degree at most ...
TERENCE TAO, TAMAR ZIEGLER
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The arithmetic derivative and Leibniz-additive functions [PDF]
, 2018 An arithmetic function $f$ is Leibniz-additive if there is a completely multiplicative function $h_f$, i.e., $h_f(1)=1$ and $h_f(mn)=h_f(m)h_f(n)$ for all positive integers $m$ and $n$, satisfying $$ f(mn)=f(m)h_f(n)+f(n)h_f(m) $$ for all positive ...
Haukkanen, Pentti +2 more
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