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pro vyhledávání: '"Webster, Jonathan A."'
Autor:
Shallue, Andrew, Webster, Jonathan
We report that there are $49679870$ Carmichael numbers less than $10^{22}$ which is an order of magnitude improvement on Richard Pinch's prior work. We find Carmichael numbers of the form $n = Pqr$ using an algorithm bifurcated by the size of $P$ wit
Externí odkaz:
http://arxiv.org/abs/2401.14495
Autor:
Sorenson, Jonathan, Webster, Jonathan
We state a general purpose algorithm for quickly finding primes in evenly divided sub-intervals. Legendre's conjecture claims that for every positive integer $n$, there exists a prime between $n^2$ and $(n+1)^2$. Oppermann's conjecture subsumes Legen
Externí odkaz:
http://arxiv.org/abs/2401.13753
Autor:
Helmreich, Chloe, Webster, Jonathan
In 1977, Hugh Williams studied Lucas pseudoprimes to all Lucas sequences of a fixed discriminant. These are composite numbers analogous to Carmichael numbers and they satisfy a Korselt-like criterion: $n$ must be a product of distinct primes and $p_i
Externí odkaz:
http://arxiv.org/abs/2306.17691
Autor:
Gouvêa, Fernando Q., Webster, Jonathan
The problem of the "common inessential discriminant divisors" attracted the attention of Dedekind, Kronecker, and Hensel in the early days of algebraic number theory. Four sources are particularly important: Dedekind's announcement, in 1871, of the s
Externí odkaz:
http://arxiv.org/abs/2108.05327
Autor:
Gouvêa, Fernando Q., Webster, Jonathan
Dedekind's theorem connecting ideal theory and polynomial congruences appears in all textbooks on algebraic number theory, but few books note its connection to the problem of ``common index divisors.'' As part of a project to study the history of thi
Externí odkaz:
http://arxiv.org/abs/2107.08905
Publikováno v:
Integers 21 (2021), #A92
Let $M(n)$ denote the number of distinct entries in the $n \times n$ multiplication table. The function $M(n)$ has been studied by Erd\H{o}s, Tenenbaum, Ford, and others, but the asymptotic behaviour of $M(n)$ as $n \to \infty$ is not known precisely
Externí odkaz:
http://arxiv.org/abs/1908.04251
Let $p(n)$ denote the smallest prime divisor of the integer $n$. Define the function $g(k)$ to be the smallest integer $>k+1$ such that $p(\binom{g(k)}{k})>k$. So we have $g(2)=6$ and $g(3)=g(4)=7$. In this paper we present the following new results
Externí odkaz:
http://arxiv.org/abs/1907.08559
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Let $k\ge 1$ be an integer, and let $P= (f_1(x), \ldots, f_k(x) )$ be $k$ admissible linear polynomials over the integers, or \textit{the pattern}. We present two algorithms that find all integers $x$ where $\max{ \{f_i(x) \} } \le n$ and all the $f_
Externí odkaz:
http://arxiv.org/abs/1807.08777
Autor:
Shallue, Andrew, Webster, Jonathan
Publikováno v:
Open Book Series 2 (2019) 411-423
We provide a new algorithm for tabulating composite numbers which are pseudoprimes to both a Fermat test and a Lucas test. Our algorithm is optimized for parameter choices that minimize the occurrence of pseudoprimes, and for pseudoprimes with a fixe
Externí odkaz:
http://arxiv.org/abs/1806.08697