Skip to content
Related Articles

Related Articles

Improve Article

Sum of each element raised to (prime-1) % prime

  • Last Updated : 03 May, 2021

Given an array arr[] and a positive integer P where P is prime and non of the elements of array are divisible by P. Find sum of all the elements of the array raised to the power P – 1 i.e. arr[0]P – 1 + arr[1]P – 1 + … + arr[n – 1]P – 1 and print the result modulo P.
Examples: 
 

Input: arr[] = {2, 5}, P = 3 
Output:
22 + 52 = 29 and 29 % 3 = 2
Input: arr[] = {5, 6, 8}, P = 7 
Output:
 

 

Approach: This problem is a direct application of Fermats’s Little Theorem, a(P-1) = 1 (mod p) where a is not divisible by P. Since, non of the elements of array arr[] are divisible by P, each element arr[i] will give the value 1 with the given operation. 
Therefore, our answer will be 1 + 1 + … (upto n(size of array)) = n.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <iostream>
#include <vector>
 
using namespace std;
 
// Function to return the required sum
int getSum(vector<int> arr, int p)
{
    return arr.size();
}
 
// Driver code
int main()
{
    vector<int> arr = { 5, 6, 8 };
    int p = 7;
    cout << getSum(arr, p) << endl;
     
    return 0;
}
 
// This code is contributed by Rituraj Jain

Java




// Java implementation of the approach
public class GFG {
 
    // Function to return the required sum
    public static int getSum(int arr[], int p)
    {
        return arr.length;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int arr[] = { 5, 6, 8 };
        int p = 7;
        System.out.print(getSum(arr, p));
    }
}

Python3




# Python3 implementation of the approach
# Function to return the required sum
def getSum(arr, p) :
     
    return len(arr)
 
# Driver code
if __name__ == "__main__" :
     
    arr = [5, 6, 8]
    p = 7
    print(getSum(arr, p))
 
# This code is contributed by Ryuga

C#




// C# implementation of the approach
 
using System;
 
public class GFG{
     
    // Function to return the required sum
    public static int getSum(int []arr, int p)
    {
        return arr.Length;
    }
 
    // Driver code
    static public void Main (){
        int []arr = { 5, 6, 8 };
        int p = 7;
        Console.WriteLine(getSum(arr, p));
    }
     
//This Code is contributed by akt_mit   
}

PHP




<?php
// PHP implementation of the approach
 
// Function to return the required sum
function getSum($arr, $p)
{
    return count($arr);
}
 
// Driver code
$arr = array( 5, 6, 8 );
$p = 7;
echo (getSum($arr, $p));
 
// This code is contributed
// by Sach_Code
?>

Javascript




<script>
 
    // Javascript implementation of the approach
     
    // Function to return the required sum
    function getSum(arr, p)
    {
        return arr.length;
    }
     
    let arr = [ 5, 6, 8 ];
    let p = 7;
    document.write(getSum(arr, p));
 
</script>
Output: 
3

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :