毕达哥拉斯四重奏详细介绍

本文概述

C ++
Java
Python3
C#
的PHP

给定4分, 检查它们是否构成勾股四重奏。
【毕达哥拉斯四重奏详细介绍】它定义为整数a, b, c, d的元组, 使得

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。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|。

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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

# Pythoncode 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# 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：