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Number Theory Summary 2012-09-05

Relatively dull, a little bit number theory took a long time to figure out, a small summary.① Greatest Common divisor (Euclidean method)Function gcd (a,b:longint): Longint;BeginIf B=0 then Gcd:=aelse GCD:=GCD (b,a mod b);End② least common multipleLCM (A, B) *gcd (A, b) =a*bLCM (A, B) =a*b/gcd (A, b);③ primes tableSieve method④ Prime number TestMiller-rabbin Test:If present and n coprime positive integer A satisfies a^ (n-1) =1 (

C. Beautiful Numbers

OUTPUT1165/*题目:Beautifulnumber链接:http://codeforces.com/contest/300题意:给两个数a,b;如果某个数的每一位上都是由a或b组成如:a=1,b=3;则n=113那么n就是goodnumber;如果某个数满足是goodnumber;且各个位上的数的和,也是goodnumber;那么这个数称为excellentnumber;求n长度的位数的数,有多少个满足a,b的excellentnumber;结果%(10^9+7);思路:排列组合的方法;首先n个长度的数s,必须是若干个a,b组成的每一位上;所以设有x个a,y个b,那么x*a+y*b==s;x+y==n;所以枚举处所有的x,y=n-x;所以也可以求出s=a*x+y*b;然后判断s是否每一位上都是a或者b;如果是的话,那么排列组合x在n中的组合方法数;*/#include#include#include#include#include#include#include#include#include#includetypedef__int64ll;usingnamespacest

Preliminary study on Golang modules

go ignores the Gopath and vendor folders, depending only on the go.mod download. Auto or not set, the GO command enables or disables module support based on the current directory. Module support is enabled only if the current directory is outside of GOPATH/SRC and itself contains a Go.mod file or is located in a directory that contains go.mod files. Defining a Module Who doesn't know how to use it when it starts? But go has provided me with a tool that can be entered in the console: go h

Avionics OJ-2035 people to see people love a^b

People See people love a^b Problem Description An integer representing the last three digits of the a^b. Description: The meaning of A^b is "A's B-square" Input data contains multiple test instances, one row per instance, consisting of two positive integers a and B (1B=0, it indicates the end of the input data and does not handle it. Output for each test instance, print the last three bits of the a^b that represent the integers, one row for each output. Sample Input 2 3 12 6

Linux Kernel Programming: Defensive programming learning

/* *kernel : Linux2.6.32.63 *file : \scripts\mod\modpost.h \scripts\mod\modpost.c *author : Davidlin *date : 2014-12-25pm *email : [email protected] or [email protected] *world : the City of SZ, inch *ver : 000.000.001 *history: Editor time do * 1) Linpeng 2014-12-25 created this file! * 2) */

UbuntuLinux: Apache installation settings

UbuntuLinux: Apache installation settings-Linux Enterprise Application-Linux server application information. For details, refer to the following section. Install Apache2 Sudo apt-get install apache2 Edit the/etc/apache2/apache2.conf file. before modifying the file, back up the configuration file. In this way, you can recover an error. AddDefaultCharset ISO-8859-1 => AddDefaultCharset GB2312 In this way, we won't go through the garbled code every time we open the web page! Add the security M

Medusa crack ssh Password

From accidentally climbing the blog It hurts. as you write your hand, medusa is still quick to crack. First, let's take a look at the help. Root @ perl-exploit:/pentest/exploits/framework3 # medusaMedusa v1.5 [http://www.foofus.net] (C) JoMo-Kun/Foofus Networks ALERT: Host information must be supplied. Syntax: medusa [-h host |-H file] [-u username |-U file] [-p password |-P file] [-C file]-M module [OPT]-H [TEXT]: Target hostname or IP address-H [FILE]: File containing target hostnames or IP a

2 The pattern of the positive power end number

2 positive Powers-2, 4, 8, 16, 32, 64, 128, 256, ...-at the end of the numbers follow an obvious rule: 2, 4, 8, 6, 2, 4, 8, 6, .... These 4 numbers are always going to loop. In addition to the last number there is a loop-actually the final m bit-a power of 2 starting at 2m. For example, there is a loop of length 20 for the last two digits starting at 04, and a loop of length 100 for the last 3 digits starting from 008.In this article, I will show you why there are these loops, how long they are,

HDU 5794 A Simple Chess (Lucas + DP)

; - Const intN = 1e2 +5; - ConstLL mod =110119; - structData { + LL x, y; - BOOL operatorConstdata CMP)Const { + returnx = = cmp.x? Y cmp.x; A } at }q[n]; -LL F[mod +5];//factorial - Dp[n]; - - ll Pow (ll A, ll N, ll MoD) { -LL res =1; in while(n) { - if(N 1) tores = res * A%MoD; +A = a *

HDU 4869 Turn The Pokers (combination number + Fermat theorem)

-1)/a = 1/a%p get a^ (p-2) = 1/a%pdid you find it? This turns an integer into a denominator! so he got sum+= ((f[m]%mod) * (Quickmod ((f[i]*f[m-i)) %mod,mod-2)%mod)1#include 2#include 3#include 4#include 5#include 6 using namespacestd;7 #defineN 1000068 #definell Long Long9 #defineMOD 1000000009Ten ll N,m; One ll A[n];

Linux Kernel Programming: Defensive programming learning

/**kernel:linux2.6.32.63*file:\scripts\mod\ Modpost.h\scripts\mod\modpost.c *author:davidlin*date :2014-12-25pm*Email :[emailprotected]or[emailprotected] *world:thecityofSZ,inChina *Ver:000.000.001 *history:editor timedo *NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;1) linpeng 2014-12-25createdthisfile! NBSP;NBSP;*NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;NBSP;2) *//*Linuxkernelcode: modpost.hmodpost.c,

[Openwrt Project Development Notes]: PHP + Nginx installation (7)

updateopkg install php5 php5-mod-apc opkg install php5-mod-gd php5-mod-session opkg install php5-mod-pdo-mysql php5-mod-pdo php5-mod-mysql opkg install php5-mod-mcrypt php5-

Extended Lucas theorem

i64 POW (i64 a,i64 b,i64 MoD) {i64 ans=1; while(b) {if(b1) ans=ans*a%MoD; A=a*a%MoD; b>>=1; } returnans;} I64 POW (i64 a,i64 b) {i64 ans=1; while(b) {if(b1) ans=ans*A; A=a*A; b>>=1; } returnans;} I64 exgcd (i64 a,i64 b,i64x,i64 y) {i64 t,d; if(!b) {x=1; Y=0; returnA; } d=EXGCD (b,a%b,x,y); T=x; X=y; Y=t-a/b*y; returnD;}BOOLModular (i64 a[],i64 m[],i64

Euclidean veritas, extended Euclidean and modular linear equations.

Euclidean algorithm: A fast algorithm for the greatest common divisor of two integers. That is what is commonly referred to as the "Euclidean method". Given two integers a, b. Euclid can find A, B greatest common divisor in the complexity of log (max (|a|, |b|)) in the worst possible degree. The computational method of time complexity is also very interesting, see "Introduction to Algorithms".Prove the correctness of Euclid's algorithm:A can be expressed as A = kb + R, and r = a

Multiplication Inverse element

operational rules for modulesArithmetic RulesThe modulo operation is somewhat similar to the basic arithmetic, but with the exception of division. The rules are as follows: (A + b)% P = (a% p + b% p)% p (1) (A-a)% P = (a% p-b p)% P (2) (A * b)% P = (a% p * b% p)% P (3) (A^B) % P = ((a% p) ^b)% P (4) Binding Law: ((a+b)% p + c)% P = (A + (b+c)% p)% P (5) ((a*b)% P * C)% P = (A * b*c)% P (6)//(A%p*b )%p= (A*B)%p Exchange Law: (A + b)% P = (b+a)% P (7) (A * b)% P = (b * A)% P (8) Distributive Law:

The seajs module depends on loading and module execution, and the seajs module depends on loading.

. preload = function (callback) {var preloadmod = data. preload var len = preloadmod. length if (len) {Module. use (preloadmod, function () {// Remove the loaded preload modules preloadmod. sp Lice (0, len) // Allow preload modules to add new preload modules Module. preload (callback)}, data. cwd + "_ preload _" + cid ()} else {callback ()} // Use function is equal to load a anonymous moduleModule. use = function (ids, callback, uri) {var mod = Module

HDU-6333 problem B. Harvest of Apples Mo Team

'ch'9') x=x*Ten+ch-'0', ch=GetChar (); returnx=f?-x:x;}//#define _DEBUG; //*//#ifdef _debugfreopen ("input","R", stdin);//freopen ("Output.txt", "w", stdout);#endif/*-----------------------Show Time----------------------*/ #defineBel (x) ((x-1)/b+1)Const intMAXN = 1e5+9; Const intB =233; Const intMOD = 1e9+7; ll ANS[MAXN]; structNode {intn,m; intID; } P[MAXN]; ll x, y; voidEXGCD (ll a,ll b) {if(b==0) {X=1; Y =0; return; } exgcd (B,a%b);

HDU 5446 Unknown Treasure Lucas theorem + Chinese remainder theorem

combination on a line.Sample Input19 5 23 5Sample OUTPUT6Source2015 ACM/ICPC Asia Regional Changchun OnlineRecommendhujie | We have a carefully selected several similar problems for you:5842 5841 5840 5839 5838 Analysis: According to Lucas solution each I:C (n,m)%pi, and then according to the The state surplus theorem integrates these results. will be able to get answers. Note that the Chinese remainder theorem calculates a value of 1 for the least common multiple of the current remainder and o

Anti-theft chain settings

Apache Web Server (standalone host user)Apache Web Server (Virtual host user) # will RewriteEngine mode open rewriteengineon# Modify the /discuz for your forum directory address in the following statement, If the program is placed in the root directory, change /discuz to /RewriteBase/discuz#Rewrite system rules do not modify Rewritecond %{query_string}^ (. *) $RewriteRule ^article-([0-9]+)-([0-9]+) \.html$portal.php?mod=view aid=$1page=$2%1rewritecond

Bzoj 2154 Crash Digital table (Möbius inversion and optimization)

DescriptionToday's math class, crash children learn least common multiple (Least Common multiple). For two positive integers a and B,LCM (A, b) represent the smallest positive integers that can be divisible by A and b at the same time. For example, the LCM (6, 8) = 24. Back home, crash still thinking about class school, in order to study least common multiple, he drew a n*m form. A number is written in each lattice, where the lattice in column J of Row I is written in the LCM (i, J). A 4*5 table

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