# Java Program for How to check if a given number is Fibonacci number?

• Last Updated : 06 Dec, 2018

Given a number ‘n’, how to check if n is a Fibonacci number. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ..

Examples :

```Input : 8
Output : Yes

Input : 34
Output : Yes

Input : 41
Output : No
```

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

Following is an interesting property about Fibonacci numbers that can also be used to check if a given number is Fibonacci or not.
A number is Fibonacci if and only if one or both of (5*n2 + 4) or (5*n2 – 4) is a perfect square (Source: Wiki).

 `// Java program to check if x is a perfect square`` ` `class` `GFG {``    ``// A utility method that returns true if x is perfect square``    ``static` `boolean` `isPerfectSquare(``int` `x)``    ``{``        ``int` `s = (``int``)Math.sqrt(x);``        ``return` `(s * s == x);``    ``}`` ` `    ``// Returns true if n is a Fibonacci Number, else false``    ``static` `boolean` `isFibonacci(``int` `n)``    ``{``        ``// n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both``        ``// is a perfect square``        ``return` `isPerfectSquare(``5` `* n * n + ``4``) || isPerfectSquare(``5` `* n * n - ``4``);``    ``}`` ` `    ``// Driver method``    ``public` `static` `void` `main(String[] args)``    ``{``        ``for` `(``int` `i = ``1``; i <= ``10``; i++)``            ``System.out.println(isFibonacci(i) ? i + ``" is a Fibonacci Number"``                                              ``: i + ``" is a not Fibonacci Number"``);``    ``}``}``// This code is contributed by Nikita Tiwari`

Output:

```1 is a Fibonacci Number
2 is a Fibonacci Number
3 is a Fibonacci Number
4 is a not Fibonacci Number
5 is a Fibonacci Number
6 is a not Fibonacci Number
7 is a not Fibonacci Number
8 is a Fibonacci Number
9 is a not Fibonacci Number
10 is a not Fibonacci Number
```

Please refer complete article on How to check if a given number is Fibonacci number? for more details!

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