Divisibility by 11: Proving the Alternating Sum Method

[Mattofix]

Homework Statement

what is the test to to see if a number is divisible by 11 and prove it.

The Attempt at a Solution

If the alternating sum of a numbers digits is divisble by 11 then so is the number.


I don't know how to prove it tho.

 

[Dick]

Do a simple case. Take a two digit number n. First digit a, second digit b. So n=a*10+b. Rewrite this as n=a*10+((b-a)+a)=a*10+a+(b-a). Now a*10+a is always divisible by 11 (why?). So if (b-a) is divisible by 11, then n is.

 

[Mattofix]

because it equals 11a.

thanks!