Fermat's little theorem in C++

Fermat’s little theorem −

This theorem states that for any prime number p,

          A^p - p is a multiple of p.

This statement in modular arithmetic is denoted as,        

          a^p  ≡ a (mod p)

If a is not divisible by p then,

 a^{p - 1} ≡ 1 (mod p)

In this problem, we are given two numbers a and p. Our task is to verify fermat’s little theorem on these values.

We need to check if a^p  ≡ a (mod p) or a^{p - 1} ≡ 1 (mod p)

Holds true for the given values of a and p.

Let’s take an example to understand the problem,

Input: a = 3, p = 7

Output: True

Explanation: 

A^p-1  ≡ 1 (mod p)

=> 3⁶ ≡ 729

=> 729 - 1 = 728

=> 728 / 7 = 104

Program to illustrate the working of theorem, 

Example

Live Demo

#include <iostream>
#include <math.h>
using namespace std;

int fermatLittle(int a, int p) {
   
   int powVal;
   if(a % p == 0){
     
      powVal = pow(a, p);
      if((powVal - p) % p == 0){
         cout<<"Fermat's little theorem holds true!";
      }
      else{
         cout<<"Fermat's little theorem holds false!";
      }
   }  
   else {
      powVal = pow(a, (p - 1));
      if((powVal - 1) % p == 0 ){
       cout<<"Fermat's little theorem holds true!";
      }
      else{
         cout<<"Fermat's little theorem holds false!";
      }
   }
     
}

int main()
{
   int a = 3, m = 11;
   fermatLittle(a, m);
   return 0;
}

Output −

Fermat's little theorem holds true!

sudhir sharma

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Updated on: 22-Jan-2021

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