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# Verify if there exists some constructive integers X and Y such that P^X is the same as Q^Y

Given two integers P and Q, the duty is to test whether or not a pair (P, Q) is equal or not, and a pair is alleged to be equal if there exist some constructive integers X and Y such that PX = QY.

Examples:

Enter: P = 16 , Q = 4
Output: Sure
Clarification: Let X = 2 and Y = 4. Thus, PX = 162 = 256 and QY = 44 = 256 . Thus, the pair (16,4) is equal.

Enter: P = 12 , Q = 24
Output: No

Method: The issue will be solved primarily based on the next statement:

For PX = QY to be true for some integer pair (X, Y),  any one of many under circumstances should be true:

1. There should exist some integer Okay, such that
2. X = Y = 0

Now to implement this, under algorithm can be utilized:

• Discover most(max) and minimal(min) quantity for 2 integer.
• Iterate a loop and test if max and min is equal or max is divisible by min, then pair of integer is equal and break from the loop.
• In any other case, pair of integer just isn’t equal.

Under is the implementation of the above strategy.

## Java

 ` `  `import` `java.io.*;` `import` `java.util.*;` ` `  `public` `class` `GFG {` ` `  `    ` `    ` `    ``public` `static` `void` `test(``int` `p, ``int` `q)` `    ``{` `        ``int` `max = Math.max(p, q);` `        ``int` `min = Math.min(p, q);` `        ``whereas` `(``true``) {` `            ``if` `(max == min) {` `                ``System.out.println(``"Sure"``);` `                ``break``;` `            ``}` `            ``if` `(max % min != ``0``) {` `                ``System.out.println(``"No"``);` `                ``break``;` `            ``}` `            ``int` `temp = max / min;` `            ``max = Math.max(temp, min);` `            ``min = Math.min(temp, min);` `        ``}` `    ``}` ` `  `    ` `    ``public` `static` `void` `primary(String[] args)` `    ``{` `        ``int` `P = ``16``;` `        ``int` `Q = ``4``;` ` `  `        ` `        ``test(P, Q);` `    ``}` `}`

Time Complexity: O(N)
Auxiliary Area: O(1)

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