检查数字的平方是否可被K整除

给定两个整数X和K ，任务是确定X ²是否可被K整除。在此， K和X都可以在[1,10 ¹⁸ ]范围内。

例子：

Input: X = 6, K = 9 
Output: YES 
Explanation: 
Since 6² is equal to 36, which is divisible by 9.

Input: X = 7, K = 21 
Output: NO 
Explanation: 
Since 7² is equal to 49, which is not divisible by 21. 
 

方法：
如上所述， X可以在[1,10 ¹⁸ ]范围内，因此我们不能直接检查X ²是否可被K整除，因为它会导致内存溢出。因此，有效的方法是首先计算X和K的最大公约数。计算完GCD后，我们将其作为可以除以X和K的最大部分。用GCD还原K，然后检查X是否可被还原的K整除。

下面是上述方法的实现：

C++

// C++ implementation to
// check if the square of X is
// divisible by K
 
#include 
using namespace std;
 
// Function to return if
// square of X is divisible
// by K
void checkDivisible(int x, int k)
{
    // Finding gcd of x and k
    int g = __gcd(x, k);
 
    // Dividing k by their gcd
    k /= g;
 
    // Check for divisibility of X
    // by reduced K
    if (x % k == 0) {
        cout << "YES\n";
    }
    else {
        cout << "NO\n";
    }
}
 
// Driver Code
int main()
{
    int x = 6, k = 9;
    checkDivisible(x, k);
 
    return 0;
}

Java

// Java implementation to
// check if the square of X is
// divisible by K
 
class GFG{
 
// Function to return if
// square of X is divisible
// by K
static void checkDivisible(int x, int k)
{
    // Finding gcd of x and k
    int g = __gcd(x, k);
 
    // Dividing k by their gcd
    k /= g;
 
    // Check for divisibility of X
    // by reduced K
    if (x % k == 0)
    {
        System.out.print("YES\n");
    }
    else
    {
        System.out.print("NO\n");
    }
}
static int __gcd(int a, int b)
{
    return b == 0 ? a : __gcd(b, a % b);    
}
 
// Driver Code
public static void main(String[] args)
{
    int x = 6, k = 9;
    checkDivisible(x, k);
}
}
 
// This code is contributed by gauravrajput1

Python3

# Python3 implementation to
# check if the square of X is
# divisible by K
 
from math import gcd
 
# Function to return if
# square of X is divisible
# by K
def checkDivisible(x, k):
     
    # Finding gcd of x and k
    g = gcd(x, k)
 
    # Dividing k by their gcd
    k //= g
 
    # Check for divisibility of X
    # by reduced K
    if (x % k == 0):
        print("YES")
    else:
        print("NO")
 
# Driver Code
if __name__ == '__main__':
     
    x = 6
    k = 9
    checkDivisible(x, k);
     
# This code is contributed by Bhupendra_Singh

C#

// C# implementation to check
// if the square of X is
// divisible by K
using System;
 
class GFG{
 
// Function to return if
// square of X is divisible
// by K
static void checkDivisible(int x, int k)
{
     
    // Finding gcd of x and k
    int g = __gcd(x, k);
 
    // Dividing k by their gcd
    k /= g;
 
    // Check for divisibility of X
    // by reduced K
    if (x % k == 0)
    {
        Console.Write("YES\n");
    }
    else
    {
        Console.Write("NO\n");
    }
}
 
static int __gcd(int a, int b)
{
    return b == 0 ? a : __gcd(b, a % b);    
}
 
// Driver Code
public static void Main(String[] args)
{
    int x = 6, k = 9;
     
    checkDivisible(x, k);
}
}
 
// This code is contributed by Princi Singh

Javascript

 
// Javascript implementation to
// check if the square of X is
// divisible by K
 
// Return gcd of two numbers
function gcd(a, b)
{
    return b == 0 ? a : gcd(b, a % b);
}
 
// Function to return if
// square of X is divisible
// by K
function checkDivisible(x, k)
{
     
    // Finding gcd of x and k
    var g = gcd(x, k);
 
    // Dividing k by their gcd
    k /= g;
 
    // Check for divisibility of X
    // by reduced K
    if (x % k == 0)
    {
        document.write("YES");
    }
    else
    {
        document.write("NO");
    }
}
 
// Driver code
var x = 6, k = 9;
checkDivisible(x, k);
 
// This code is contributed by Ankita saini
    

输出：

YES

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