Codeforces Round #368 (Div. 2)C. Pythagorean Triples
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Katya studies in a fifth grade. Recently her class studied right triangles and the Pythagorean theorem. It appeared, that there are triples of positive integers such that you can construct a right triangle with segments of lengths corresponding to triple. Such triples are calledPythagorean triples.
For example, triples (3, 4, 5), (5, 12, 13) and (6, 8, 10) are Pythagorean triples.
Here Katya wondered if she can specify the length of some side of right triangle and find any Pythagorean triple corresponding to such length? Note that the side which length is specified can be a cathetus as well as hypotenuse.
Katya had no problems with completing this task. Will you do the same?
The only line of the input contains single integer n (1 ≤ n ≤ 109) — the length of some side of a right triangle.
Print two integers m and k (1 ≤ m, k ≤ 1018), such that n, m and k form a Pythagorean triple, in the only line.
In case if there is no any Pythagorean triple containing integer n, print - 1 in the only line. If there are many answers, print any of them.
3
4 5
6
8 10
1
-1
17
144 145
67
2244 2245
Illustration for the first sample.
题意:给出一个数a 求两个数b和c使得a,b,c为勾股数
来自百度知道的证明:证明
/* ***********************************************Author : rycCreated Time : 2016-08-21 SundayFile Name : E:\acm\codeforces\368C.cppLanguage : c++Copyright 2016 ryc All Rights Reserved************************************************ */#include<iostream>#include<cstdio>#include<cstdlib>#include<cstring>#include<algorithm>#include<cmath>#include<queue>#include<list>#include<vector>#include<map>#include<stack>using namespace std;typedef long long LL;typedef pair<int,int>pii;const int maxn=1000010;int main(){ LL n;cin>>n; if(n<3ll){ printf("-1\n"); } else { LL k=n/2ll; if(n&1){ printf("%lld %lld\n",2ll*(k*k+k),2ll*(k*k+k)+1); } else { printf("%lld %lld\n",k*k-1,k*k+1); } } return 0;}
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