## A number theory problem

Forum for the GRE subject test in mathematics.
huayualice
Posts: 15
Joined: Thu Sep 11, 2014 7:19 am

### A number theory problem

The following number has a missing digit x.

n=13645x04142250.

If n has a remainder 5 when divided by 11 then x = ____.

Solution: 0-5+2-2+4-1+4-0+x-5+4-6+3-1 = 5 (mod 11).

What theorem/rule did the solution use?

Thanks!

DDswife
Posts: 161
Joined: Thu Aug 14, 2014 5:29 pm

### Re: A number theory problem

It is using the rule to test if a number is divisible by 11

A is number is divisible by 11? Think of the numbers you know. Think of what happens when you multiply a number by 11. Or google for it. But the rule is like this: add every other digit, add the ones you skip. Substract the two numbers you got. If you get a multiple of 11, then the original number was divisible by 11

Example

123456789

Add the odd numbers. You get 25
Add the even numbers. You get 20
Substract them. The difference is not a multiple of 11. Hencem the number is not a multiple of 11

http://www.mathsisfun.com/divisibility-rules.html

huayualice
Posts: 15
Joined: Thu Sep 11, 2014 7:19 am

### Re: A number theory problem

Thank you very much!

DDswife
Posts: 161
Joined: Thu Aug 14, 2014 5:29 pm

### Re: A number theory problem

You're welcome! If you have more doibts, just ask them