Find Integer
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 687 Accepted Submission(s): 78
Special Judge
Problem Description
people in USSS love math very much, and there is a famous math problem .
give you two integers n,a,you are required to find 2 integers b,c such that an+bn=cn.
Input
one line contains one integer T;(1≤T≤1000000)
next T lines contains two integers n,a;(0≤n≤1000,000,000,3≤a≤40000)
Output
print two integers b,c if b,c exits;(1≤b,c≤1000,000,000);
else print two integers -1 -1 instead.
Sample Input
1 2 3
Sample Output
4 5
Source
1、首先介绍一下费马大定理:当n>2时,a^n+b^n=c^n 一定没有正整数解。
2、奇偶数列法则:当n==2时
平方整数解a^2+b^2=c^2的a值奇偶数列法则、
当a为奇数时,
a=2n+1
c=n^2+(n+1)^2
b=c-1
当a为偶数时,
a=2n+2,
c=1+(n-1)^2
b=c-2