最简分数p/q在b进制下的小数为无限小数的充要条件是
q不完全由b的某些因子乘积构成
#include<bits/stdc++.h> #define rre(i,r,l) for(int i=(r);i>=(l);i--) #define re(i,l,r) for(int i=(l);i<=(r);i++) #define Clear(a,b) memset(a,b,sizeof(a)) #define inout(x) printf("%d",(x)) #define douin(x) scanf("%lf",&x) #define strin(x) scanf("%s",(x)) #define op operator typedef unsigned long long ULL; typedef const int cint; typedef long long LL; using namespace std; template<typename Q> void inin(Q &x) { x=0;int f=0;char ch=getchar(); while(ch<'0'||ch>'9'){if(ch=='-')f=1;ch=getchar();} while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar(); x=f?-x:x; } LL gcd(LL a,LL b) { LL c; while(a%b) { c=a%b; a=b,b=c; } return b; } int main() { // freopen("a.in","r",stdin); // freopen("a.out","w",stdout); LL p,q,b,t; inin(t); while(t--) { inin(p),inin(q),inin(b); if(!p){cout<<"Finite\n";continue;} LL d=gcd(q,p); q/=d; while(q%b==0)q/=b; d=gcd(q,b); while(d>1) { while(!(q%d)) q/=d; d=gcd(b,q); } if(q==1)cout<<"Finite\n"; else cout<<"Infinite\n"; } return 0; }