Check if a Number Can be Expressed as a^b in Python

Suppose we have a number n. We have to check whether we can make express it like a^b or not.

So, if the input is like 125, then the output will be True as 125 = 5^3, so a = 5 and b = 3

To solve this, we will follow these steps −

• if num is same as 1, then:
  • return true
• for initialize i := 2, when i * i <= num, update (increase i by 1), do:
  • val := log(num) / log(i)
  • if val - integer part of val is nearly 0, then:
    • return true
• return false

Let us see the following implementation to get better understanding −

Example

Live Demo

#include<iostream>
#include<cmath>
using namespace std;

bool solve(int num) {
   if (num == 1)
      return true;
 
   for (int i = 2; i * i <= num; i++) {
      double val = log(num) / log(i);
      if ((val - (int)val) < 0.00000001)
         return true;
   }
   
   return false;
}
 
int main() {
   int n = 125;
   cout << solve(n);
}

Input

125

Output

1