check if a number is a Fibonacci number in Java

Mathematics for Programming Numbers (Article) Numbers (Program)

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• Understanding Fibonacci Numbers: Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two. For example, the sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, ...

• Steps to Check for Fibonacci Numbers:

  • Determine if the number belongs to the Fibonacci sequence.
  • One way to check is to iterate through Fibonacci numbers until you find a number greater than or equal to the given number. If it matches the given number, then it's a Fibonacci number.

Given Input:

13

Expected Output:

13 is a Fibonacci number.

Program:

public class FibonacciChecker {
    public static boolean isPerfectSquare(int x) {
        int s = (int) Math.sqrt(x);
        return s * s == x;
    }
    
    public static boolean isFibonacci(int number) {
        // A number is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both is a perfect square
        return isPerfectSquare(5 * number * number + 4) || isPerfectSquare(5 * number * number - 4);
    }
    
    public static void main(String[] args) {
        int number = 13; // Example number to check
        
        if (isFibonacci(number)) {
            System.out.println(number + " is a Fibonacci number.");
        } else {
            System.out.println(number + " is not a Fibonacci number.");
        }
    }
}

Output:

13 is a Fibonacci number.

Explanation:

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