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

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:2

2^{2}+ 5^{2}= 29 and 29 % 3 = 2

Input:arr[] = {5, 6, 8}, P = 7

Output:3

**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 ` |

*chevron_right*

*filter_none*

## 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)); ` ` ` `} ` `} ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` `} ` |

*chevron_right*

*filter_none*

## 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 ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

3

## Recommended Posts:

- Count occurrences of a prime number in the prime factorization of every element from the given range
- Larger of a^b or b^a (a raised to power b or b raised to power a)
- Check for an array element that is co-prime with all others
- Find First element in AP which is multiple of given prime
- Sum of element whose prime factors are present in array
- Nearest element with at-least one common prime factor
- All possible co-prime distinct element pairs within a range [L, R]
- Check if each element of the given array is the product of exactly K prime numbers
- K-th digit in 'a' raised to power 'b'
- Find value of y mod (2 raised to power x)
- Number of digits in 2 raised to power n
- Print last k digits of a^b (a raised to power b)
- Check if a number can be expressed as x^y (x raised to power y)
- Find multiple of x closest to or a ^ b (a raised to power b)
- Find unit digit of x raised to power y

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.