# Nicomachu’s Theorem

Nicomachu’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 Nicomachu's Theorem  #include  using namespace std;     void NicomachuTheorum_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;      NicomachuTheorum_sum(n);      return 0;  }

## Java

 // Java program to verify Nicomachu's Theorem  import java.io.*;     class GFG {         static void NicomachuTheorum_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;          NicomachuTheorum_sum(n);      }  }     // This code is contributed by anuj_67.

## Python3

 # Python3 program to verify  # Nicomachu's Theorem     def NicomachuTheorum_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;  NicomachuTheorum_sum(n);     # This code is contributed   # by mits

## C#

 // C# program to verify  // Nicomachu's Theorem  using System;      class GFG {          static void NicomachuTheorum_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;          NicomachuTheorum_sum(n);      }  }      // This code is contributed by anuj_67

## PHP

 

Output:

Yes


My Personal Notes arrow_drop_up Maths is the language of nature

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Improved By : PawanMeena, vt_m, Mithun Kumar