# Find (a^b)%m where ‘a’ is very large in C++

C++Server Side ProgrammingProgramming

In this tutorial, we are going to solve the equation (ab)%m﻿ where a is a very large number.

The equation (ab)%m=(a%m)*(a%m)...b_times. We can solve the problem by finding the value of a%m and then multiplying it b﻿ times.

Let's see the steps to solve the problem.

• Initialize the numbers a, b, and m.

• Write a function to find the a%m﻿.

• Initialize the number with 0.

• Iterate over the number in string format.

• Add the last digits to the number.

• Update the number with number modulo them.

• Get the value of a%m﻿.

• Write a loop that iterates b times.

• Multiply the a%m﻿ and modulo the result with m.

• Print the result.

## Example

Let's see the code.

Live Demo

#include<bits/stdc++.h>
using namespace std;
unsigned int aModm(string str, unsigned int mod) {
unsigned int number = 0;
for (unsigned int i = 0; i < str.length(); i++) {
number = number * 10 + (str[i] - '0');
number %= mod;
}
return number;
}
unsigned int aPowerBmodM(string &a, unsigned int b, unsigned int m) {
unsigned int a_mod_m_result = aModm(a, m);
unsigned int final_result = 1;
for (unsigned int i = 0; i < b; i++) {
final_result = (final_result * a_mod_m_result) % m;
}
return final_result;
}
int main() {
string a = "123456789012345678901234567890123";
unsigned int b = 3, m = 7;
cout << aPowerBmodM(a, b, m) << endl;
return 0;
}

## Output

If you execute the above program, then you will get the following result.

1

## Conclusion

If you have any queries in the tutorial, mention them in the comment section.

Published on 01-Feb-2021 11:41:29