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HDU5391威尔逊定理
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威爾遜定理 當且僅當p為素數,p | (p-1)!+1
若p為合數,則p=a*b;如果a!=b,那么p|(p-1)!,
如果a=b,如果p為4,那么p|(p-1)!=2,如果p大于4,那么sqrt§和sqrt(2q)肯定屬于(p-1)!中,可以整除
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<climits>
#include<cctype>
#include<queue>
#include<set>
#include<ctime>using namespace std
;typedef long long ll
;
const int INF
=0x3f3f3f3f;
const int MAXN
=1e5+5;ll
mult(ll a
, ll b
, ll p
) {a
%= p
;b
%= p
;ll res
= 0, tmp
= a
;while(b
) {if (b
& 1) {res
+= tmp
;if (res
> p
) res
-= p
;}tmp
<<= 1;if (tmp
> p
) tmp
-= p
;b
>>= 1;}return res
;
}ll
quick_pow(ll a
, ll b
, ll p
) {ll res
= 1;ll tmp
= a
% p
;while(b
) {if (b
& 1) res
= mult(res
, tmp
, p
);tmp
= mult(tmp
, tmp
, p
);b
>>= 1;}return res
;
}bool check(ll a
, ll n
, ll x
, ll t
) {ll res
= quick_pow(a
, x
, n
);ll last
= res
;for (ll i
= 1; i
<= t
; i
++) {res
= mult(res
, res
, n
);if (res
== 1 && last
!= 1 && last
!= n
-1) return true;last
= res
;}return res
!= 1;
}bool Miller_Rabin(ll n
) {if (n
< 2) return false;if (n
== 2) return true;if ((n
& 1) == 0) return false;ll x
= n
-1;ll t
= 0;while ((x
& 1) == 0) {x
>>= 1;t
++;}srand(time(NULL));const ll tims
= 8;for (ll i
= 0; i
< tims
; i
++) {ll a
= rand() % (n
-1) + 1;if (check(a
, n
, x
, t
)) return false;}return true;
}int main()
{int T
,n
;scanf("%d",&T
);while(T
--){scanf("%d",&n
);if(n
==4){printf("2\n");}else if(Miller_Rabin(n
)){printf("%d\n",n
-1);}else{printf("0\n");}}return 0;
}
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