How we find last digit of fibonacci ?

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How we find last digit of fibonacci n.. Assume that n is maximum "10^19"..

I know that, in fibonacci last digit is periodical.. in 60 period..

FOR EXAMPLE
fibo[61]
fibo[1]
fibo[121]
fibo[181] ..... all of them finish with number "1".

How we find last digit in "0,5" second ?

I have a code like that.. with "long" and "BigInteger"

C#

import java.util.Scanner;
public class Main {
   public static void main(String[] args) {
       Scanner input = new Scanner (System.in);

       long n;
       while(input.hasNextLong()){
           n = input.nextLong();
           if(n >= 60) n %= 60;
           long fibo_1 = 0;
           long fibo_2 = 1;
           long fibo_3;
           for(long i = 0; i < n; i++){
               fibo_3 = fibo_1 + fibo_2;
               fibo_1 = fibo_2;
               fibo_2 = fibo_3 % 10;
           }
           System.out.println(fibo_2);
       }
   }
}

Posted 21-Oct-13 3:53am

Steven Gerrard

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Comments

Kenneth Haugland 21-Oct-13 10:15am

I dont understand your code: Are you trying to calcualte the last digit in the fibonacci numbers? If so there is a lot of values that you dont need to store, but you still need to calcualte the Fibonacci numbers the normal way.

Steven Gerrard 21-Oct-13 16:44pm

Yes.. I am trying to calcualte the last digit in the fibonacci numbers

nv3 21-Oct-13 11:06am

And what exactly is your question? If your program works, you have answered your own question, haven't you?

And by the way, what is a useful application for that?

Ed Nutting 21-Oct-13 12:31pm

I can answer the second bit for him: solving his homework. The "0.5 seconds" requirement just screams "theoretical h/w question"!

Ed :)

Steven Gerrard 21-Oct-13 16:45pm

can u compile this prg in 0.5 second ?? if u can't, don't talk more.. You don't know me

Steven Gerrard 21-Oct-13 16:48pm

if u want to learn anything, or want to give any advice u can write. This is not my homework

Ed Nutting 21-Oct-13 16:54pm

Compile or run? Or both? I can do both if you like :p You're right, I don't know you, but I have an impression of you. If you don't like the impression I have got, you should consider the way you present yourself, not the way that I respond. In practical terms, you ought to flesh out your question more and perhaps even comment your code. Anyway, I hope your problem is solved.

Ed

Ed Nutting 21-Oct-13 12:44pm

Your code for generating the Fibonacci sequence would be fine if you just removed the "% 10". Put the "% 10" outside the loop i.e. "println(fibo_2 % 10)" which should then get you the answer you want.

I suggest you read this: http://www.math.toronto.edu/mccann/assignments/199S/FibModK.pdf
If you don't understand at least the first page, then you should give up on this problem.
If you understand the first page, but don't bother reading the rest because you think you already know it, give up programming.
If you understand all of it but can't solve your problem, go ask on a maths forum for a better explanation.

All the best,
Ed

Advice on a crude but perhaps more obvious method: Generate an array of last digits for n=1 to 60, then when asked for last digit of Xth element, index into your array at X%60. Job done.

nv3 21-Oct-13 13:45pm

My virtual 5.

Ed Nutting 21-Oct-13 13:46pm

:)

Steven Gerrard 21-Oct-13 16:43pm

Thanks bro

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