Nicomachus’s Theorem states that sum of cubes of first n natural numbers is equal to squares of natural number sum.
In other words
Or we can say that the sum is equal to square of n-th triangular number.
Mathematical Induction based proof can be found here.
C++
// CPP program to verify Nicomachus's Theorem#include <bits/stdc++.h>using namespace std;void NicomachusTheorem_sum(int n){ // Compute sum of cubes int sum = 0; for (int k=1; k<=n; k++) sum += k*k*k; // Check if sum is equal to // given formula. int triNo = n*(n+1)/2; if (sum == triNo * triNo) cout << "Yes"; else cout << "No";}// driver functionint main(){ int n = 5; NicomachuTheorem_sum(n); return 0;} |
Java
// Java program to verify Nicomachus's Theoremimport java.io.*;class GFG { static void NicomachuTheorem_sum(int n) { // Compute sum of cubes int sum = 0; for (int k = 1; k <= n; k++) sum += k * k * k; // Check if sum is equal to // given formula. int triNo = n * (n + 1) / 2; if (sum == triNo * triNo) System.out.println("Yes"); else System.out.println("No"); } // driver function public static void main (String[] args) { int n = 5; NicomachuTheorem_sum(n); }}// This code is contributed by anuj_67. |
Python3
# Python3 program to verify# Nicomachus's Theoremdef NicomachuTheorem_sum(n): # Compute sum of cubes sum = 0; for k in range(1, n + 1): sum += k * k * k; # Check if sum is equal to # given formula. triNo = n * (n + 1) / 2; if (sum == triNo * triNo): print("Yes"); else: print("No");# Driver Coden = 5;NicomachuTheorem_sum(n);# This code is contributed # by mits |
C#
// C# program to verify// Nicomachus's Theoremusing System; class GFG { static void NicomachuTheorem_sum(int n) { // Compute sum of cubes int sum = 0; for (int k = 1; k <= n; k++) sum += k * k * k; // Check if sum is equal to // given formula. int triNo = n * (n + 1) / 2; if (sum == triNo * triNo) Console.WriteLine("Yes"); else Console.WriteLine("No"); } // Driver Code public static void Main () { int n = 5; NicomachuTheorem_sum(n); }} // This code is contributed by anuj_67 |
PHP
<?php// PHP program to verify// Nicomachus's Theoremfunction NicomachuTheorem_sum($n){ // Compute sum of cubes $sum = 0; for ($k = 1; $k <= $n; $k++) $sum += $k * $k * $k; // Check if sum is equal to // given formula. $triNo = $n * ($n + 1) / 2; if ($sum == $triNo * $triNo) echo "Yes"; else echo "No";} // Driver Code $n = 5; NicomachuTheorem_sum($n);// This code is contributed by anuj_67.?> |
Javascript
<script>// JavaScript program to verify Nicomachus's Theorem function NicomachuTheorem_sum(n) { // Compute sum of cubes let sum = 0; for (let k = 1; k <= n; k++) sum += k * k * k; // Check if sum is equal to // given formula. let triNo = n * (n + 1) / 2; if (sum == triNo * triNo) document.write("Yes"); else document.write("No"); } // Driver code let n = 5; NicomachuTheorem_sum(n); // This code is contributed by souravghosh0416.</script> |
Output:
Yes
Time complexity : O(n)
Auxiliary Space : O(1)
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