Triplet pair (a, b, c) such that a+b, b+c and a+c are all divisible by K

Given two integers ‘N’ and ‘K’, the task is to count the number of triplets (a, b, c) of positive integers not greater than ‘N’ such that ‘a+b’, ‘b+c’ and ‘c+a’ are all multiples of ‘K’. Note that ‘a’, ‘b’ and ‘c’ may or may not be the same in a triplet pair.

Examples:

Input: N = 2, K = 2
Output: 1
All possible triplets are
(1, 1, 1) and (2, 2, 2)



Input: N = 3, K = 2
Output: 9

Approach: Run three nested loops from ‘1’ to ‘N’ and check whether i+j, j+l and l+i are all divisible by ‘K’. Increment the count if the condition is true.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include<iostream>
using namespace std;
class gfg
{
    // Function returns the
    // count of the triplets
    public:
    long count_triples(int n, int k);
};
   
    long gfg :: count_triples(int n, int k)
    {
        int i = 0, j = 0, l = 0;
        int count = 0;
  
        // iterate for all
        // triples pairs (i, j, l)
        for (i = 1; i <= n; i++)
        {
            for (j = 1; j <= n; j++)
            {
                for (l = 1; l <= n; l++)
                {
  
                    // if the condition
                    // is satisfied
                    if ((i + j) % k == 0
                        && (i + l) % k == 0
                        && (j + l) % k == 0)
                        count++;
                }
            }
        }
        return count;
    }
  
    // Driver code
    int main()
    {
        gfg g;
        int n = 3;
        int k = 2;
        long ans = g.count_triples(n, k);
        cout << ans;
    }
//This code is contributed by Soumik

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Java

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// Java implementation of the approach
class GFG {
  
    // Function returns the
    // count of the triplets
    static long count_triples(int n, int k)
    {
        int i = 0, j = 0, l = 0;
        int count = 0;
  
        // iterate for all
        // triples pairs (i, j, l)
        for (i = 1; i <= n; i++) {
            for (j = 1; j <= n; j++) {
                for (l = 1; l <= n; l++) {
  
                    // if the condition
                    // is satisfied
                    if ((i + j) % k == 0
                        && (i + l) % k == 0
                        && (j + l) % k == 0)
                        count++;
                }
            }
        }
        return count;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int n = 3;
        int k = 2;
        long ans = count_triples(n, k);
        System.out.println(ans);
    }
}

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Python3

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# Python3 implementation of the 
# above approach
def count_triples(n, k): 
      
    count, i, j, l = 0, 0, 0, 0
  
    # Iterate for all triples 
    # pairs (i, j, l) 
    for i in range(1, n + 1):
        for j in range(1, n + 1): 
            for l in range(1, n + 1): 
                  
                # If the condition 
                # is satisfied 
                if ((i + j) % k == 0 and
                    (i + l) % k == 0 and
                    (j + l) % k == 0): 
                    count += 1
          
    return count 
  
# Driver code 
if __name__ == "__main__"
      
    n, k = 3, 2
    ans = count_triples(n, k) 
    print(ans) 
      
# This code is contributed 
# by Rituraj Jain

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C#

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// C# implementation of the approach
  
using System;
  
class GFG {
   
    // Function returns the
    // count of the triplets
    static long count_triples(int n, int k)
    {
        int i = 0, j = 0, l = 0;
        int count = 0;
   
        // iterate for all
        // triples pairs (i, j, l)
        for (i = 1; i <= n; i++) {
            for (j = 1; j <= n; j++) {
                for (l = 1; l <= n; l++) {
   
                    // if the condition
                    // is satisfied
                    if ((i + j) % k == 0
                        && (i + l) % k == 0
                        && (j + l) % k == 0)
                        count++;
                }
            }
        }
        return count;
    }
   
    // Driver code
    public static void Main()
    {
        int n = 3;
        int k = 2;
        long ans = count_triples(n, k);
        Console.WriteLine(ans);
    }
}

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PHP

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<?php
//PHP implementation of the approach 
// Function returns the 
// count of the triplets 
function count_triples($n, $k
    
         $i = 0; $j = 0; $l = 0; 
        $count = 0; 
  
        // iterate for all 
        // triples pairs (i, j, l) 
        for ($i = 1; $i <= $n; $i++) { 
            for ($j = 1; $j <= $n; $j++) { 
                for ($l = 1; $l <= $n; $l++) { 
  
                    // if the condition 
                    // is satisfied 
                    if (($i + $j) % $k == 0 
                        && ($i + $l) % $k == 0 
                        && ($j + $l) % $k == 0) 
                        $count++; 
                
            
        
        return $count
    
  
    // Driver code 
        $n = 3; 
        $k = 2; 
        $ans = count_triples($n, $k); 
        echo ($ans); 
      
// This code is contributed by ajit
?>

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Output:

9


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