Check whether a number is a Fibonacci number or not JavaScript

We are required to write a JavaScript function that takes in a number and returns a boolean based on the fact whether or not it comes in the fibonacci series.

For example −

If the function call is like this −

fibonacci(12);
fibonacci(89);
fibonacci(55);
fibonacci(534);

Then the output should be −

false
true
true
false

What is the Fibonacci Series?

The Fibonacci series is a sequence where each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Method 1: Using Recursive Approach

Now, let's write a recursive solution to this problem:

const fibonacci = (query, count = 1, last = 0) => {
    if(count 

false
true
true
false


Method 2: Using Iterative Approach

A more efficient iterative solution that generates Fibonacci numbers until we reach or exceed the query:

function isFibonacci(n) {
    if (n === 0 || n === 1) return true;
    
    let a = 0, b = 1;
    
    while (b 

false
true
true
true
true


Method 3: Using Mathematical Formula

A number n is Fibonacci if one of (5*n² + 4) or (5*n² - 4) is a perfect square:

function isPerfectSquare(n) {
    let sqrt = Math.sqrt(n);
    return sqrt === Math.floor(sqrt);
}

function isFibonacciMath(n) {
    return isPerfectSquare(5*n*n + 4) || isPerfectSquare(5*n*n - 4);
}

console.log(isFibonacciMath(55));
console.log(isFibonacciMath(89));
console.log(isFibonacciMath(12));
console.log(isFibonacciMath(100));


true
true
false
false


Comparison

Conclusion

The iterative approach is most practical for checking Fibonacci numbers, offering good performance and readability. The mathematical method is fastest but harder to understand.