2018中国大学生程序设计竞赛 - 网络选拔赛 -Find Integer（费马大定理）

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

2018中国大学生程序设计竞赛 - 网络选拔赛

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