大偶数表为一个素数与一个殆素数之和:素数属于某个等差数列

余新河猜想蕴涵了哥得巴赫猜想。对以任给定的正整数为模的余新河猜想，本文证明了与［１－３］中关于哥得巴赫猜想的定理同样强的结果．     

Sums of Five Almost Equal Prime Squares

Let Pi, 1≤i≤5, be prime numbers. It is proved that every integer N that satisfies N=5 （mod 24） can be written as N=p1^2＋p2^2＋P3^2＋p4^2 ＋p5^2, where │√N5-Pi│≤N^1/2-19/850＋∈.     

素数幂、双素数幂阶元的共轭类长的个数为4的 有限群的结构

设群G为一个有限群.如果群G中素数幂、双素幂阶元的共轭类长的集合为{1,p~a,m,p~bm},那么群G是可解的,其中ab为正整数,p为素数且与m互素.进一步,给出了群G/Z(G)的结构,这是对文"Chen R F,Zhao X H.A criterion for a group to have nilpotent p-complements[J].Monatsh Math,2016,179(2):221-225"中定理A主要结论的一个推广.     

Small prime solutions of a pair of linear equations in five prime variables

Assume an additional congruent condition on the coefficients. We prove that the pair 5 of linear equations ∑j=1^5 αλjpj = bλ （λ= 1, 2） has solutions in primes pj satisfying pj 〈〈 （｜b1｜＋｜b2｜＋1） maxλ,j ｜αλj｜^2318＋ε. This improves the exponent 79680 without assuming the additional condition of the second author＇s.     

数论中切比雪夫不等式的一点补充

利用Wallis不等式,得到素数计算函数的一个下界估计.     

Sums of primes and quadratic linear recurrence sequences

Let u be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on u in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expressible by the sum of a prime number and an element of u has a positive lower density. This criterion is then checked for some second order linear recurrence sequences. It follows, for instance, that the set of positive integers of the form p ＋ [（2 ＋ √3）n], where p is a prime number and n is a positive integer, has a positive lower density. This generalizes a recent result of Enoch Lee. In passing, we show that the periods of linear recurrence sequences of order m modulo a prime number p cannot be ＂too small＂ for most prime numbers p.     

新的素数检测方法

提出了一个快速而简单的素数检测方法,它的时间复杂性为O(log^(3+ε)N)这里0<ε≤1,空间复杂性为O(logN),N≡3(mod 4)时,时间复杂性为O(log(3+ε)N)这里0<ε≤1,空间复杂性为O(logN),N≡3(mod 4)时,时间复杂性为O(log^(2+ε)N),是迄今为止最快的多项式算法.     

二项式系数幂和序列在模p2下的几个性质

利用同余理论和多项式理论研究二项式系数幂和序列在模p2下的同余性质,得到了一些非平凡结果.为进一步研究二项式系数幂和序列的多项式递推公式提供有利的工具.     

一个素变数的Diophantine不等式(Ⅲ)

令.本文证明了存在N（c）＞0,对任意实数N＞N（c）,不等式有素数解p1,p2,p3,其中c1为一绝对正常数．     

Chen’s Conjecture and Its Generalization

Let l1, l2, ..., lg be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k ≤ x such that （k ＋l1）^2, （k ＋l2）^2, ..., （k ＋lg）^2 can not be expressed as 2^n＋p^α is at least c（g）x, where p is an odd prime and the constant c（g） depends only on g.