Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C++ Program to Implement Fermat’s Little Theorem
Fermat's little theorem is one of the fundamental results of elementary number theory and is the basis for the Fermat primality test. The theorem is named after Pierre de Fermat, who stated it in 1640. The Theorem states that if p is a prime number, then for any integer a, the number a p–a is an integer multiple of p.
Algorithm
Begin Function power() is used to compute a raised to power b under modulo M function modInverse() to find modular inverse of a under modulo m : Let m is prime If a and m are relatively prime, then modulo inverse is a^(m - 2) mod m End
Example Code
#include <iostream>
using namespace std;
int pow(int a, int b, int M) {
int x = 1, y = a;
while (b > 0) {
if (b % 2 == 1) {
x = (x * y);
if (x > M)
x %= M;
}
y = (y * y);
if (y > M)
y %= M;
b /= 2;
}
return x;
}
int modInverse(int a, int m) {
return pow(a, m - 2, m);
}
int main() {
int a, m;
cout<<"Enter number to find modular multiplicative inverse: ";
cin>>a;
cout<<"Enter Modular Value: ";
cin>>m;
cout<<modInverse(a, m)<<endl;
}Output
Enter number to find modular multiplicative inverse: 26 Enter Modular Value: 7 3
Updated on: 30-Jul-2019
509 Views
Advertisements