# Thread: Prove that x is divisible by 11 if alternate sum is divisible by 11

1. ## Prove that x is divisible by 11 if alternate sum is divisible by 11

Question: Let x= (dkdk-1...d1d0)10

Prove that x is divisible by 11 if and only if the following alternating sum is divisible by 11.

d0-d1+d2-d3+...+(-1)kdk

Any help is appreciated!

2. ## Re: Prove that x is divisible by 11 if alternate sum is divisible by 11

Originally Posted by oregongirl
Question: Let x= (dkdk-1...d1d0)10

Prove that x is divisible by 11 if and only if the following alternating sum is divisible by 11.

d0-d1+d2-d3+...+(-1)kdk

Any help is appreciated!
expand your decimal form as a sum of powers of 10.

replace 10 by (11 - 1) and expand out using the binomial expansion. Apply mod 11

see where that takes you