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Program to check whether a number is Proth number or not in C++
Given with a number ‘n’ and the task is to determine whether the given positive integer is a proth or not and display the result as an output.
What is Proth Number?
A proth number is given by
$$N=k\cdot\:2^{n}+1$$
Where, n is a positive integer and k is a odd positive integer
The first few proth numbers are given below −
3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97.......
Input
number: 17
Output
its a proth number
Input
number: 18
Output
its not a proth number
Approach used in the given program is as follows
Input the number to check for the condition
Apply the given formula to check whether its a proth number or not
If the condition holds true print its a proth number
If the condition doesn’t holds true print its not a proth number
Algorithm
Step 1→ declare function to calculate power of 2 bool isPower(int num) return (num && !(num & (num - 1))) Step 2→ Declare function to check if a number is a proth number or not bool isProth(int num) declare int k = 1 While (k < (num / k)) IF (num % k == 0) IF (isPower(num / k)) return true End Set k = k + 2 End End return false Step 3→ In main() Declare int num = 17 IF (isProth(num - 1)) Print "its a proth number" End Else Print "its not a proth number" End
Example
#include <bits/stdc++.h>
using namespace std;
//function to calculate power of 2
bool isPower(int num){
return (num && !(num & (num - 1)));
}
//function to check if a number is a proth number
bool isProth(int num){
int k = 1;
while (k < (num / k)){
if (num % k == 0){
if (isPower(num / k))
return true;
}
k = k + 2;
}
return false;
}
int main(){
int num = 17;
if (isProth(num - 1))
cout << "its a proth number";
else
cout << "its not a proth number";
return 0;
}Output
If run the above code it will generate the following output −
its a proth number
Updated on: 13-Aug-2020
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