IS FIBO........

Problem Statement

You are given an integer, N. Write a program to determine if N is an element of the Fibonacci sequence.

The first few elements of the Fibonacci sequence are 0,1,1,2,3,5,8,13,⋯. A Fibonacci sequence is one where every element is a sum of the previous two elements in the sequence. The first two elements are 0 and 1.

Formally: 

fib0fib1⋮fibn=0=1=fibn−1+fibn−2∀n>1

Input Format 
The first line contains T, number of test cases. 
T lines follow. Each line contains an integer N.

Output Format 
Display IsFibo if N is a Fibonacci number and IsNotFibo if it is not. The output for each test case should be displayed in a new line.

Constraints 
1≤T≤105 
1≤N≤1010

Sample Input

3
5
7
8

Sample Output

IsFibo
IsNotFibo
IsFibo

Explanation 
5 is a Fibonacci number given by fib5=3+2 
7 is not a Fibonacci number 
8 is a Fibonacci number given by fib6=5+3

SOLUTION:

import java.math.BigDecimal;

import java.math.RoundingMode;

import java.util.*;

public class FibonacciTester {

    private static BigDecimal zero = BigDecimal.valueOf(0);

    private static BigDecimal one = BigDecimal.valueOf(1);

    private static BigDecimal two = BigDecimal.valueOf(2);

    private static BigDecimal four = BigDecimal.valueOf(4);

    private static BigDecimal five = BigDecimal.valueOf(5);

    public static void main(String[] args) {

       

       Scanner sc=new Scanner(System.in);

       int t=sc.nextInt(); 

       while(t!=0){

        BigDecimal num =sc.nextBigDecimal();

        if (isFibonacci(num)) {

            System.out.println("IsFibo");

        } else {

            System.out.println("IsNotFibo");

        }

       t=t-1;

       }

    }   

        

    public static boolean isFibonacci(BigDecimal num) {

        if (num.compareTo(zero) <= 0) {

            return false;

        }

        BigDecimal base = num.multiply(num).multiply(five);

        BigDecimal possibility1 = base.add(four);

        BigDecimal possibility2 = base.subtract(four);

        return (isPerfectSquare(possibility1) || isPerfectSquare(possibility2));

    }

    public static boolean isPerfectSquare(BigDecimal num) {

        BigDecimal low = zero;

        BigDecimal high = num;

        while (low.compareTo(high) <= 0) {

            BigDecimal mid = low.add(high).divide(two).setScale(0, RoundingMode.DOWN);

            BigDecimal square = mid.multiply(mid);

            int comparison = square.compareTo(num);

            if (comparison == 0) {

                return true;

            } else if (comparison > 0) {

                high = mid.subtract(one);

            } else {

                low = mid.add(one);

            }

        }

        return false;

    }

}