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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Supercongruences involving Motzkin numbers and central trinomial coefficients
莫茨金数 中心三项式系数 超同余
2023/4/21
In this talk, we investigate congruence properties for Motzkin numbers and central trinomial coefficients. Let M_n and T_n denote the nth Motzkin number and the nth central trinomial coefficient respe...
商洛学院数学与计算机应用学院初等数论课件Chapter 1 Prime Numbers.
An integer $n$ is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we char...
Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers
Mersenne numbers cyclotomic cosets of 2 modulo n Poulet pseudoprime super-Poulet pseudoprime overpseudoprime
2012/6/19
We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $...
A Cesaro Average of Hardy-Littlewood numbers
Goldbach-type theorems Hardy-Littlewood numbers Laplace transforms Cesaro averages
2012/6/14
Let $\Lambda$ be the von Mangoldt function and (r_{\textit{HL}}(n) = \sum_{m_1 + m_2^2 = n} \Lambda(m_1),) be the counting function for the Hardy-Littlewood numbers. Let $N$ be a sufficiently large in...
A Cesaro Average of Goldbach numbers
Goldbach-type theorems Laplace transforms Cesaro averages
2012/6/14
Let $\Lambda$ be the von Mangoldt function and (r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2)) be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer. We prove that ...
A determinant of generalized Fibonacci numbers
generalized Fibonacci numbers Cassini’s identity determinant evaluation
2012/4/18
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of the...
Given a finite set $S$ of places of a number field, we prove that the field of totally $S$-adic algebraic numbers is not Hilbertian.
The irregular distribution of primes up to 300,000 in the sequence of odd numbers
prime distribution of primes
2011/9/19
In this paper we listed a sequence of odd numbers up to 300,000 by a computer calculating and it could be find that the density of prime numbers is decreased as odd number increases and that there exi...
The distribution of pseudo prime numbers up to 300,000 in pseudo sequence of odd numbers
prime pseudo prime distribution of pseudo primes
2011/9/19
In this paper a pseudo sequence of odd numbers had been advanced, and the number of pseudo prime numbers in it are largely less than the real prime numbers in the real sequence of odd numbers. This ps...
FORTRAN source program calculating the Goldbach-Xu’s numbers with recursive method
Goldbach’s conjecture Goldbach-Xu’s number prime distribution of primes
2011/9/19
In this paper we have presented two source programs with FORTRAN 90 language to calculate the distribution of prime numbers in the sequence of odd numbers and the Goldbach-Xu’s numbers for every even ...
C++ source program calculating the Goldbach-Xu’s numbers with recursive method
Goldbach’s conjecture Goldbach-Xu’s number prime distribution of primes source program
2011/9/19
In this paper we have presented two source programs with C++ to calculate the distribution of prime numbers in the sequence of odd numbers and the Goldbach-Xu’s numbers for every even number respectiv...
A FORTRAN source program for calculating the Polignac-Xu’s numbers with the recursive method
Problem of Goldbach’s conjecture type Polignac-Xu’s number prime distribution of primes
2011/9/19
In the field of number theory, in addition to Goldbach’s conjecture, there is another similar problem: Is there an even number >2 which is not the difference of two primes? An American mathematics T. ...
Abstract: The main topic of this contribution is the problem of counting square-free numbers not exceeding $n$. Before this work we were able to do it in time (Comparing to the Big-O notation, Soft-O ...
An Algorithm to Generate Square-Free Numbers and to Compute the Moebius Function
Mobius function square-free numbers zeta function Riemann hypothesis
2011/9/19
Abstract: We introduce an algorithm that iteratively produces a sequence of natural numbers k_i and functions b_i. The number k_(i+1) arises as the first point of discontinuity of b_i above k_i. We de...