费马大定理
people in USSS love math very much, and there is a famous math problem .
give you two integers nn
,aa
,you are required to find 22
integers bb
,cc
such that anan
+bn=cnbn=cn
.Inputone line contains one integer TT
;(1≤T≤1000000)(1≤T≤1000000)
next TT
lines contains two integers nn
,aa
;(0≤n≤1000(0≤n≤1000
,000000
,000,3≤a≤40000)000,3≤a≤40000)
Outputprint two integers bb
,cc
if bb
,cc
exits;(1≤b,c≤1000(1≤b,c≤1000
,000000
,000)000)
;
else print two integers -1 -1 instead.Sample Input
1 2 3
Sample Output
4 5
费马大定理,当n>2 时 a^n+b^n=c^n 无解
所以可以分为三种情况当n=0 题目说了 b和c必须>=1
n=1 b。c 解不唯一
当n=2 就是勾股定理了---->勾股数组
当a为大于1的奇数2n+1时,b=2n^2+2n, c=2n^2+2n+1
当a为大于4的偶数2n时,b=n^2-1, c=n^2+1
#include<cstdio> #include<cstring> #include<iostream> using namespace std; int main() { int t; long long n,a,b,c; scanf("%d",&t); while(t--) { scanf("%lld%lld",&n,&a); if(n==0) printf("-1 -1\n"); else if(n==1) printf("%lld %lld",a+1,2*a+1); else if(n==2) { if(a%2==1) { long long x=(a-1)/2; b=2*x*x+2*x; c=2*x*x+2*x+1; printf("%lld %lld\n",b,c); } if(a%2==0) { int x=a/2; b=x*x-1; c=x*x+1; printf("%lld %lld\n",b,c); } } else printf("-1 -1\n"); } return 0; }