Super-Poulet number is a Poulet number (pseudoprime) to base 2 if each and every divisor D divides 
.
Some of the super-poulet numbers are:
341, 1387, 2047, 2701, 3277, 4033….
Check if N is a Super-poulet number
Given an integer N, the task is to check N is a Super-Poulet Number.
Examples:
Input: N = 341
Output: Yes
Input: N = 10
Output: No
Approach: The idea is to generate all the divisors of the number N and for all divisor check D divides 
. If this condition satisfy for all divisors then the number is super-poulet number.
For Example:
For N = 341,
Divisors of 341 are {1, 11, 31, 341} and,
Similarly,also gives integer value.
Therefore, 341 is a super-poulet number.
also gives integer value. Below is the implementation of the above approach:
C++
// C++ implementation to// check if N is a super Poulet number#include <bits/stdc++.h>using namespace std;// Function to find the divisorsvector<int> findDivisors(int n){ vector<int> divisors; // Loop to iterate over the // square root of the N for (int i = 1; i < (sqrt(n) + 1); i++) { if (n % i == 0) { // Check if divisors are equal if (n / i == i) divisors.push_back(i); else { divisors.push_back(i); divisors.push_back((n / i)); } } } sort(divisors.begin(), divisors.end()); return divisors;}// Function to check if N// is a super Poulet numberbool isSuperdNum(int n){ vector<int> d = findDivisors(n); // Loop to check that every // divisor divides 2^D - 2 for (int i : d) { double x = (pow(2, i) - 2) / i; if (floor(x) != x) return false; } return true;}// Driver Codeint main(){ int n = 341; if (isSuperdNum(n) == true) cout << "Yes"; else cout << "No";}// This code is contributed by phasing17. |
Java
// Java implementation to// check if N is a super Poulet numberimport java.util.*;class GFG { // Function to find the divisors static ArrayList<Integer> findDivisors(int n) { ArrayList<Integer> divisors = new ArrayList<Integer>(); // Loop to iterate over the // square root of the N for (int i = 1; i < (Math.sqrt(n) + 1); i++) { if (n % i == 0) { // Check if divisors are equal if (n / i == i) divisors.add(i); else { divisors.add(i); divisors.add((n / i)); } } } Collections.sort(divisors); return divisors; } // Function to check if N // is a super Poulet number static boolean isSuperdNum(int n) { ArrayList<Integer> d = findDivisors(n); // Loop to check that every // divisor divides 2^D - 2 for(int i : d) { double x = (Math.pow(2, i) - 2) / i; if (Math.floor(x) != x) return false; } return true; } // Driver Code public static void main(String[] args) { int n = 341; if (isSuperdNum(n) == true) System.out.print("Yes"); else System.out.print("No"); }}// This code is contributed by phasing17. |
Python3
# Python3 implementation to # check if N is a super Poulet number import math# Function to find the divisors def findDivisors(n): divisors = [] # Loop to iterate over the # square root of the N for i in range(1,\ int(math.sqrt(n) + 1)): if (n % i == 0) : # Check if divisors are equal if (n / i == i): divisors.append(i) else: divisors.append(i) divisors.append(int(n / i)) return sorted(divisors) # Function to check if N # is a super Poulet number def isSuperdNum(n): d = findDivisors(n) # Loop to check that every # divisor divides 2^D - 2 for i in d: x = (2**i-2)/i if int(x) != x: return False return True# Driver Code if __name__ == "__main__": n = 341 if isSuperdNum(n) == True: print("Yes") else : print("No") |
C#
// C# implementation to// check if N is a super Poulet numberusing System;using System.Collections.Generic;class GFG { // Function to find the divisors static List<int> findDivisors(int n) { List<int> divisors = new List<int>(); // Loop to iterate over the // square root of the N for (int i = 1; i < (Math.Sqrt(n) + 1); i++) { if (n % i == 0) { // Check if divisors are equal if (n / i == i) divisors.Add(i); else { divisors.Add(i); divisors.Add((n / i)); } } } divisors.Sort(); return divisors; } // Function to check if N // is a super Poulet number static bool isSuperdNum(int n) { List<int> d = findDivisors(n); // Loop to check that every // divisor divides 2^D - 2 foreach(int i in d) { double x = (Math.Pow(2, i) - 2) / i; if (Math.Truncate(x) != x) return false; } return true; } // Driver Code public static void Main(string[] args) { int n = 341; if (isSuperdNum(n) == true) Console.Write("Yes"); else Console.Write("No"); }}// This code is contributed by chitranayal. |
Javascript
<script>// Javascript implementation to// check if N is a super Poulet number// Function to find the divisorsfunction findDivisors(n){ let divisors = [] // Loop to iterate over the // square root of the N for(let i = 1; i < Math.floor(Math.sqrt(n) + 1); i++){ if (n % i == 0) { // Check if divisors are equal if (n / i == i){ divisors.push(i) } else{ divisors.push(i) divisors.push(Math.floor(n / i)) } } } return divisors.sort((a, b)=> a - b)} // Function to check if N// is a super Poulet numberfunction isSuperdNum(n){ let d = findDivisors(n) // Loop to check that every // divisor divides 2^D - 2 for(let i in d){ let x = (2**i - 2) / i if (Math.floor(x) != x){ return false } } return true}// Driver Code let n = 341 if(isSuperdNum(n) == true){ document.write("Yes") } else { document.write("No") }// This code is contributed by _saurabh_jaiswal</script> |
Output:
Yes
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