A number theory problem

[huayualice]

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]

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]

Thank you very much!

[DDswife]

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