共查询到17条相似文献,搜索用时 125 毫秒
1.
p阶临界2-边连通图的最大边数 总被引:2,自引:0,他引:2
设G=(V,E)是2-边连通图,若对每个点v∈V,G-v不是2-边连通图,则称G是临界2-边连通图. 本文证明了p阶临界2-边连通图的最大边数是 7, P=6; (1/8)(P~2+4p) p=0(mod 4); f(p)= (1/8)(P~2+2p+13) p=1(mod 4); (1/8)(P~2+28) p=(2mod 4),p≠6 (1/8)(P~2+2p+9) p=3(mod 4)。并且给出了达到最大边数的极值图. 相似文献
2.
For the Diophantine equation
x^4 — Dy^2 = 1 (1)
where D>0 and is not a perfect square, we prove the following theorems in this paper.
Theorem 1. If D\[{\not \equiv }\]7 (mod 8),D=p1p2...ps,s≥2,where pi(i = 1,…,s) are distincyt primes,p1≡1(mod 4) such that either 2p1=a^2+b^2,а≡\[ \pm \]3(mod 8),b三\[ \pm \]3(mod 8) or there is a j(2≤j≤s), for which Legendre
symbal \[\left( {\frac{{{p_j}}}{{{p_1}}}} \right) = - 1\],and pi≡7(mod8) (i=2,..., s) or pi≡3(mod 8) (i=2,..., s), then (1) has no solutions in positive integer x,y.
Theorem 2. If D=p1...ps,s≥2, where pi(i = 1,…,s) are distinct primes, and pi≡3(mod 4)(i = 1,…,s), then (1) has no solutions in positive integer x, y.
Theorem 3. The equation (1) with D=2p1...ps has no solutions in positive
integer x, y, if
(1) p1≡(mod 4), pi≡7(mod 8) (i = 2, ???, s), snch that either 2p1 = a^2+b^2
a≡\[ \pm \]3(mod 8),b≡\[ \pm \]3(mod 8)or there is a j (2≤j≤s),for which \[\left( {\frac{{{p_j}}}{{{p_1}}}} \right) = - 1\];
or
(2) p1≡5(mod8),pi≡3(mod8) (i = 2,..., s);
or
⑶p1≡5(mod8),pi≡7(mod 8) (i=2,…,s).
Corollary of theorem 3. If D = 2pq, p≡5(mod 8), q≡3(mod 4), where p, q
are distinct primes, then (1) has no solutions in positive integer x, y.
Theorem 4. If D=2p1...ps, pi≡3(mod 4)(0 = 1,...,s), then (1) has no solutions In positive integer x, y. 相似文献
3.
Diophantine方程y~2=px(x~2+2) 总被引:2,自引:0,他引:2
设p是大于3的奇素数.本文证明了:当p≡5或7(mod 8)时,方程y~2=px(x~2+2)无正整数解(x,y);当p≡1(mod 8)时,该方程至多有1组解;当p≡3(mod 8)时,该方程至多有2组解. 相似文献
4.
Zhang Yuanda 《数学年刊B辑(英文版)》1983,4(1):77-94
In this paper,the following theorem is proved:Let p be a prime distinet from 3 and 7,then the groups of order 2~3 p~2 have1)60 types when p=1(mod 8),2)52 types when p=5(mod 8),3)42 types when p=3,7(mod 8). 相似文献
5.
WEI DaSheng 《中国科学 数学(英文版)》2013,56(2):227-238
We propose a method to determine the solvability of the diophantine equation x2-Dy2=n for the following two cases:(1) D = pq,where p,q ≡ 1 mod 4 are distinct primes with(q/p)=1 and(p/q)4(q/p)4=-1.(2) D=2p1p2 ··· pm,where pi ≡ 1 mod 8,1≤i≤m are distinct primes and D=r2+s2 with r,s ≡±3 mod 8. 相似文献
6.
利用p次单位根e~((2πi)/p)作为原始材料,通过不同层次的组合,当p≡1(mod 4)时,给出了方程x~2+y~2=p的整数解.在此基础上,当p≡1(mod 8)时,进一步给出了x~2+2y~2=p的整数解. 相似文献
7.
窦志红 《纯粹数学与应用数学》2011,27(2):210-212,235
设p是奇素数,N(p)是椭圆曲线E:y2=2px(x2+1)的正整数点(x,y)的个数.主要讨论了N(p)的性质,运用初等方法及四次Diophantine方程的性质,对某些特殊素数p,给出了N(p)的上界.证明了当p≡1(mod 8)且p=s2+32t,其中s,t是正整数时,N(p)≤3;当p≡1(mod 8)且p+s... 相似文献
9.
WEI DaSheng 《中国科学 数学(英文版)》2014,57(1):49-60
We determine the sum of two integral squares over imaginary quadratic fields Q(√-2p),where p≡1 mod 8 is a prime satisfying 2p=r2+s2with r,s≡±3 mod 8. 相似文献
10.
WEI DaSheng 《中国科学 数学(英文版)》2014,(1)
We determine the sum of two integral squares over imaginary quadratic fields Q(√-2p),where p≡1 mod 8 is a prime satisfying 2p=r2+s2with r,s≡±3 mod 8. 相似文献
11.
设D_1=multiply from i=1 to s q_i(s=1或2),q_i≡-1(mod6)(i=1,2,…,s)是彼此不同的奇素数,p≡1(mod6)为奇素数.运用初等方法讨论了丢番图方程x~3±1=3·2~αpD_1y~2(α=0或1)的正整数解的情况. 相似文献
12.
13.
有穷正级亚纯函数的T方向和Borel方向 总被引:6,自引:0,他引:6
对任意正数λ,正整数q_1和q_2,记E_1={argz=θ_j|0∣θ_1<θ_2<…<θ_(q1)<2π}及E_2={axgz=φ_j|0■1<φ2<…<φq2<2π},使得E_1∩E_2=■,则(1)存在复平面上的λ级亚纯函数f(z),恰以E_1∪E_2为其T方向且恰以E_2为其Borel方向,(2)存在复平面上的级与下级均为λ的亚纯函数g(z),恰以E_1∪E_2为其Borel方向且恰以E_2为其T方向. 相似文献
14.
For any prime \(p>3,\) we prove that where \(E_{0},E_{1},E_{2},\ldots \) are Euler numbers and \(\left( \frac{\cdot }{p}\right) \) is the Legendre symbol. This result confirms a conjecture of Z.-W. Sun. We also re-prove that for any odd prime \(p,\) using WZ method.
相似文献
$$\begin{aligned} \sum _{k=0}^{p-1}\frac{3k+1}{(-8)^k}{2k\atopwithdelims ()k}^3\equiv p\left( \frac{-1}{p}\right) +p^3E_{p-3}\pmod {p^4}, \end{aligned}$$
$$\begin{aligned} \sum _{k=0}^{\frac{p-1}{2}}\frac{6k+1}{(-512)^k}{2k\atopwithdelims ()k}^3\equiv p\left( \frac{-2}{p}\right) \pmod {p^2} \end{aligned}$$
15.
在分离局部凸空间中考虑free disposal集的对偶性质,其中free disposal集是指与凸锥的代数和仍是其本身的集合.在E_1或E_2是free disposal集的条件下,证明了(E_1∩E_2)~+=E_1~++E_2~+和E_1~+∩E_2~+=(E_1+E_2)~+等对偶结果. 相似文献
16.
17.
实二次域Q(P(1/2))(p≡3(mod 4))类数的上界 总被引:1,自引:0,他引:1
设p是适合p≡3(Pod4)的奇素数,h,ε分别是实二次域Q的类数和基本单位.本文运用初等方法证明了:εh<(p+a+2)a+2/4(a+2)!,其中 相似文献