Codeforces Problem 707C Pythagorean triples (math) __ACM

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codeforces Problem 707C Pythagorean triples

accept:0 submit:0
Time Limit:1 second Memory limit:256 megabytes Problem Description

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 so you can construct a right triangle with segments of Len Gths corresponding to triple. Such triples are called Pythagorean triples.

For example, triples (3, 4, 5), (5,) and (6, 8,) are Pythagorean triples.

Here Katya wondered if she can specify the length of some side to right triangle and find any Pythagorean triple Correspon Ding to such length? Note this side which length is specified can be a cathetus as as as. Hypotenuse.

Katya had no problems with completing this task. Would you do the same?

Input

The only line of this input contains single integer n (1≤n≤10^9)-the length of some side to right triangle.
Output

Print two integers m and K (1≤m, k≤10^18), such that N, M. and K form a Pythagorean triple, in the only line.

In case if there be no any Pythagorean triple containing integer n, print-1 in the only line. If There are many answers, print any of them.
Sample Input 3
6
1
17
Sample Output 4 5
8 10
-1
144 145
2244 2245 Hint

Illustration for the.

Problem Idea

Ideas for solving problems:

Meaning
give you a number n, ask if there are another two number a,b, so that these three numbers exactly constitute the three sides of a right triangle

Type
Math problems

Analysis
For the right-angled triangle ABC, as shown in figure:

What we know is that

Because the title says if there are multiple solutions to the problem, output any one can be, so we might as well assume that the input of n is a rectangular length of the edge, then

According to the square difference formula can be

So, this time, what we're going to solve is a,b.

So, we can sort of discuss

"Time Complexity && optimization"
O (1)

Topic link →codeforces Problem 707C Pythagorean triples Source Code

/*sherlock and Watson and adler*/
#pragma comment (linker, "/stack:1024000000,1024000000")
#include < stdio.h>
#include <string.h>
#include <stdlib.h>
#include <queue>
#include <stack>
#include <math.h>
#include <vector>
#include <map>
#include < set>
#include <cmath>
#include <complex>
#include <string>
#include < algorithm>
#include <iostream>
#define EPS 1e-9
#define LL long
#define PI ACOs (-1.0 )
#define BITNUM (a) __builtin_popcount (a)
using namespace std;
const int N = 100005;
const int M =;
const int inf = 1000000007;
const int mod = 1000000007;
int main ()
{
    __int64 n,a,b;
    scanf ("%i64d", &n);
    if (n==1| | n==2)
        puts ("-1");
    else if (n*n%2)
        printf ("%i64d%i64d\n", (n*n-1)/2, (n*n+1)/2);
    else
        printf ("%i64d%i64d\n", (n*n/2-2)/2, (n*n/2+2)/2);
    return 0;
}

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