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 function int main()
{ int n = 5;
NicomachuTheorem_sum(n);
return 0;
} |
Java
// Java program to verify Nicomachus's Theorem import 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 Theorem def 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 Code n = 5 ;
NicomachuTheorem_sum(n); # This code is contributed # by mits |
C#
// C# program to verify // Nicomachus's Theorem using 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 Theorem function 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)