## Divisible By 11

#### Problem

Consider the following results.

10^{1} + 1 = 11

10^{2} 1 = 99 = 9 11

10^{3} + 1 = 1001 = 91 11

10^{4} 1 = 9999 = 909 11

10^{5} + 1 = 100001 = 9091 11

Prove that 10^{n}1 is divisible by 11 if `n` is even and 10^{n}+1 is divisible by 11 if `n` is odd.

Problem ID: 208 (17 Feb 2005) Difficulty: 3 Star