Results 1 to 10 of about 270 (42)
Annals of Mathematics and Physics, 2022 N continuous prime numbers can combine a group of continuous even numbers. If an adjacent prime number is followed, the even number will continue. For example, if we take the prime number 3, we can get an even number 6.
Linghong Xie
semanticscholar +1 more source
Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
doaj +1 more source
On the Waring-Goldbach problem for two squares and four cubes
Open Mathematics, 2023 Let NN be a sufficiently large integer. In this article, it is proved that, with at most O(N112+ε)O\left({N}^{\tfrac{1}{12}+\varepsilon }) exceptions, all even positive integers up to NN can be represented in the form p12+p22+p33+p43+p53+p63{p}_{1}^{2 ...
Zhang Min, Bai Hongxin, Li Jinjiang
doaj +1 more source
Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 [PDF]
, 2016 We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square.
A., Zaccagnini, Languasco, Alessandro
core +4 more sources
On pairs of equations involving unlike powers of primes and powers of 2
, 2020 In this paper, it is proved that every pair of sufficiently large even integers can be represented by a pair of equations, each containing one prime, one prime square, two prime cubes and 302 powers of 2. This result constitutes a refinement upon that of
Yuhui Liu
semanticscholar +1 more source
A pair of equations in unlike powers of primes and powers of 2
Open Mathematics, 2020 In this article, we show that every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of one prime, one prime squares, two prime cubes, and 187 powers of 2.
Cai Yong, Hu Liqun
doaj +1 more source
The integral part of a nonlinear form with a square, a cube and a biquadrate
Open Mathematics, 2020 In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
doaj +1 more source
Goldbach Conjecture and the least prime number in an arithmetic progression [PDF]
, 2010 In this Note, we try to study the relations between the Goldbach Conjecture and the least prime number in an arithmetic progression. We give a new weakened form of the Goldbach Conjecture.
Zhang, Shaohua
core +3 more sources
On the irregularity of the distribution of the sums of pairs of odd primes
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 6, Page 377-381, 2002., 2002 Let P2(n) denote the number of ways of writing n as a sum of two odd primes. We support a conjecture of Hardy and Littlewood concerning P2(n) by showing that it holds in a certain “average” sense. Thereby showing the irregularity of P2(n).
George Giordano
wiley +1 more source
On pairs of equations in unlike powers of primes and powers of 2
Open Mathematics, 2017 In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.
Hu Liqun, Yang Li
doaj +1 more source