本文概述
给定4分, 检查它们是否构成勾股四重奏。
它定义为整数a, b, c, d的元组, 使得
。它们基本上是丢番图方程的解。在几何解释中,它表示边长为整数的长方体|a|, |b|, |c|,其空间对角线为|d|。
此处显示的长方体侧面是毕达哥拉斯四联体的示例。
当它们的最大公约数为1时, 它是原始的。每个勾股四边形都是原始四边形的整数倍。我们可以生成一组原始的毕达哥拉斯四联体, 对于它们, a可以通过公式生成:
a = m2 + n2 – p2 – q2, b = 2(mq + np), c = 2(nq – mp), d = m2 + n2 + p2 + q2
其中m, n, p, q是最大公约数为1的非负整数, 因此m + n + p + q为奇数。因此, 所有原始毕达哥拉斯四联体的特征是勒贝格的身份.
(m2 + n2 + p2 + q2)2 =(2mq + 2nq)2 + 2(nq – mp)2 +(m2 + n2 – p2 – q2)m2 + n2 – p2 – q2
C ++
//C++ code to detect Pythagorean Quadruples.
#include <bits/stdc++.h>
using namespace std;
//function for checking
bool pythagorean_quadruple( int a, int b, int c, int d)
{
int sum = a * a + b * b + c * c;
if (d * d == sum)
return true ;
else
return false ;
}
//Driver Code
int main()
{
int a = 1, b = 2, c = 2, d = 3;
if (pythagorean_quadruple(a, b, c, d))
cout <<"Yes" <<endl;
else
cout <<"No" <<endl;
}
Java
//Java code to detect Pythagorean Quadruples.
import java.io.*;
import java.util.*;
class GFG {
//function for checking
static Boolean pythagorean_quadruple( int a, int b, int c, int d)
{
int sum = a * a + b * b + c * c;
if (d * d == sum)
return true ;
else
return false ;
}
//Driver function
public static void main (String[] args) {
int a = 1 , b = 2 , c = 2 , d = 3 ;
if (pythagorean_quadruple(a, b, c, d))
System.out.println( "Yes" );
else
System.out.println( "No" );
}
}
//This code is contributed by Gitanjali.
Python3
# Python code to detect
# Pythagorean Quadruples.
import math
# function for checking
def pythagorean_quadruple(a, b, c, d):
sum = a * a + b * b + c * c;
if (d * d = = sum ):
return True
else :
return False
#driver code
a = 1
b = 2
c = 2
d = 3
if (pythagorean_quadruple(a, b, c, d)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed
# by Gitanjali.
C#
//C# code to detect
//Pythagorean Quadruples.
using System;
class GFG {
//function for checking
static Boolean pythagorean_quadruple( int a, int b, int c, int d)
{
int sum = a * a + b * b + c * c;
if (d * d == sum)
return true ;
else
return false ;
}
//Driver function
public static void Main () {
int a = 1, b = 2, c = 2, d = 3;
if (pythagorean_quadruple(a, b, c, d))
Console.WriteLine( "Yes" );
else
Console.WriteLine( "No" );
}
}
//This code is contributed by vt_M.
的PHP
<?php
//php code to detect Pythagorean Quadruples.
//function for checking
function pythagorean_quadruple( $a , $b , $c , $d )
{
$sum = $a * $a + $b * $b + $c * $c ;
if ( $d * $d == $sum )
return true;
else
return false;
}
//Driver Code
$a = 1; $b = 2; $c = 2; $d = 3;
if (pythagorean_quadruple( $a , $b , $c , $d ))
echo "Yes" ;
else
echo "No" ;
//This code is contributed by anuj_67.
?>
输出如下:
Yes
参考文献
维基:https://en.wikipedia.org/wiki/Pythagorean_quadruple
数学世界:http://mathworld.wolfram.com/PythagoreanQuadruple.html