1
#include<iostream>
2#include<stdio.h>
3#include<cmath>
4#include<cstdlib>
5#include<algorithm>
6using namespace std;
7long long mp(long long a,long long b,long long n)
8
{
9
long long d=1,t=a;
10 while (b>0)
11
{
12 if (b%2==1) d=d*t%n;
13 b/=2;
14 t=t*t%n;
15
}
16 return d;
17
}
18long long tu, tv;
19long long Gau(double x)
20{
21 if (x+1e-8>(long long)x) return (long long)x;
22 return (long long)x-1;
23}
24int main()
25{
26 long long p, M, a, B, r, A, x, y,ta,tb;
27 while (scanf("%lld", &p) == 1)
28 {
29 if (p % 4 != 1)
30 {
31 printf("Illegal\n");
32 continue;
33 }
34 B = 1;
35 a = 2;
36 A = mp(a , (p - 1)/ 4,p);
37 while ((A * A + 1) % p != 0)
38 {
39 a++;
40 A = mp(a , (p - 1)/ 4,p);
41 }
42 M = ((A * A + 1) / p);
43 tu = A%M;
44 tv = B%M;
45 while (M>1)
46 {
47 tu=A+M*Gau(0.5-double(A)/double(M));
48 tv=B+M*Gau(0.5-double(B)/double(M));
49 r=(tu*tu+tv*tv)/M;
50 ta=abs((tu*A+tv*B)/M);
51 tb=abs((tv*A-tu*B)/M);
52 A=ta;
53 B=tb;
54 M=r;
55 }
56 if(A>B)
57 swap(A,B);
58 printf("Legal %lld %lld\n", A, B);
59 }
60}
61
62
posted on 2010-09-02 10:34
Lancelot 阅读(264)
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