## Problem:

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn[−]1 + Fn[−]2, where F1 = 1 and F2 = 1.

Hence the first 12 terms will be:

F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144

The 12th term, F12, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

4782

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 25
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

import java.math.BigInteger;

public final class p025 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p025().run());
}

private static final int DIGITS = 1000;

public String run() {
BigInteger lowerthres = BigInteger.TEN.pow(DIGITS - 1);
BigInteger upperthres = BigInteger.TEN.pow(DIGITS);
BigInteger prev = BigInteger.ONE;
BigInteger cur = BigInteger.ZERO;
int i = 0;
while (true) {
// At this point, prev = fibonacci(i - 1) and cur = fibonacci(i)
if (cur.compareTo(lowerthres) >= 0)
return Integer.toString(i);
else if (cur.compareTo(upperthres) >= 0)

prev = cur;
cur = temp;
i++;
}
}

}