Sgu 119

119. Magic Pairs

time limit per test: 0.25 sec. memory limit per test: 4096 KB

注意先%n能被n整除的ax+by那么d*ax+d*by也能因为a,b<n所以(d*ax+d*by)%n的也能被n整除，然后枚举！

“Prove that for any integer X and Y if 5X+4Y is divided by 23 than 3X+7Y is divided by 23 too.” The task is from city Olympiad in mathematics in Saratov, Russia for schoolchildren of 8-th form. 2001-2002 year.
For given N and pair (A₀, B₀) find all pairs (A, B) such that for any integer X and Y if A₀X+B₀Y is divided by N then AX+BY is divided by N too (0<=A,B<N).

Input

Each input consists of positive integer numbers N, A₀ and B₀ (N,A₀,B₀£ 10000) separated by whitespaces.

Output

Write number of pairs (A, B) to the first line of output. Write each pair on a single line in order of non-descreasing A (and B in case of equal A). Separate numbers by single space.

Sample Input

3
1 2

Sample Output

 1 #pragma comment(linker,"/STACK:102400000,102400000")
 2 #include <cstdio>
 3 #include <vector>
 4 #include <cmath>
 5 #include <queue>
 6 #include <set>
 7 #include <cstring>
 8 #include <iostream>
 9 #include <algorithm>
10 using namespace std;
11 #define INF 0x7fffffff 
12 #define mod 1000000007
13 #define ll long long
14 #define maxn 200005
15 #define pi acos(-1.0)
16 #define dis(a, b) sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y))
17 ll gcd(ll n, ll m){ return m ? gcd(m, n%m) : n; }
18 int n, m, k, c, a, b, x, y;
19 struct node{
20     int a, b;
21 }p[maxn];
22 bool cmp(node a, node b){ return (a.a < b.a || a.a == b.a&&a.b < b.b); }
23 int main(){
24     scanf("%d%d%d", &n, &a, &b);
25     a %= n; b %= n;

View Code

Author	: Michael R. Mirzayanov
Resource	: PhTL #1 Training Contests
Date	: Fall 2001

posted @ 2014-02-10 05:52 HaibaraAi 阅读(155) 评论(0) 收藏举报

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