# Check if a M-th fibonacci number divides N-th fibonacci number

Given two numbers M and N, the task is to check if the M-th and N-th Fibonacci numbers perfectly divide each other or not.

Examples:

Input: M = 3, N = 6
Output: Yes
F(3) = 2, F(6) = 8 and F(6) % F(3) = 0

Input: M = 2, N = 9
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A naive approach will be to find the N-th and M-th Fibonacci numbers and check if they are perfectly divisible or not.

An efficient approach is to use the Fibonacci property to determine the result. If m perfectly divides n, then Fm also perfectly divides Fn, else it does not.

Exception: When N is 2, it is always possible as Fibo2 is 1, which divides every other Fibonacci number.

Below is the implementation of the above approach:

 `// C++ program to check if  ` `// M-th fibonacci divides N-th fibonacci ` `#include ` `using` `namespace` `std; ` ` `  `void` `check(``int` `n, ``int` `m) ` `{ ` `    ``// exceptional case for F(2) ` `    ``if` `(n == 2 || m == 2 || n % m == 0) { ` `        ``cout << ``"Yes"` `<< endl; ` `    ``} ` `    ``// if none of the above cases, ` `    ``// hence not divisible ` `    ``else` `{ ` `        ``cout << ``"No"` `<< endl; ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `m = 3, n = 9; ` `    ``check(n, m); ` ` `  `    ``return` `0; ` `} `

 `// Java program to check ` `// if M-th fibonacci  ` `// divides N-th fibonacci ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `static` `void` `check(``int` `n, ``int` `m) ` `{ ` `    ``// exceptional case for F(2) ` `    ``if` `(n == ``2` `|| m == ``2` `|| ` `        ``n % m == ``0``)  ` `    ``{ ` `        ``System.out.println( ``"Yes"``); ` `    ``} ` `     `  `    ``// if none of the above cases, ` `    ``// hence not divisible ` `    ``else`  `    ``{ ` `        ``System.out.println( ``"No"``); ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``int` `m = ``3``, n = ``9``; ` `    ``check(n, m); ` `} ` `} ` ` `  `// This code is contributed ` `// by anuj_67. `

 `# Python 3 program to  ` `# check if M-th fibonacci  ` `# divides N-th fibonacci ` ` `  `def` `check(n, m): ` ` `  `    ``# exceptional case for F(2) ` `    ``if` `(n ``=``=` `2` `or` `m ``=``=` `2` `or` `        ``n ``%` `m ``=``=` `0``) : ` `        ``print``( ``"Yes"` `) ` `     `  `    ``# if none of the above  ` `    ``# cases, hence not divisible ` `    ``else` `: ` `        ``print``( ``"No"` `) ` ` `  `# Driver Code ` `m ``=` `3` `n ``=` `9` `check(n, m) ` ` `  `# This code is contributed ` `# by Smitha `

 `// C# program to check ` `// if M-th fibonacci  ` `// divides N-th fibonacci ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `static` `void` `check(``int` `n, ``int` `m) ` `{ ` `    ``// exceptional case for F(2) ` `    ``if` `(n == 2 || m == 2 || ` `        ``n % m == 0)  ` `    ``{ ` `         ``Console.WriteLine( ``"Yes"``); ` `    ``} ` `     `  `    ``// if none of the above cases, ` `    ``// hence not divisible ` `    ``else` `    ``{ ` `        ``Console.WriteLine( ``"No"``); ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main ()  ` `{ ` `    ``int` `m = 3, n = 9; ` `    ``check(n, m); ` `} ` `} ` ` `  `// This code is contributed ` `// by anuj_67. `

 ` `

Output:
```Yes
```

Time Complexity: O(1).

Maths is the language of nature

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Improved By : vt_m, Smitha Dinesh Semwal

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