Discrete Mathematics question

(a) Prove that for all integers n2 1, 10"(1 mod 11. (b) Use part (a) to prove that a positive integer is divisible by 11 if, and only if, the alternating sum of its digits is divisible by 11. (For instance, the alternating sum of the digits of 82,379 is 8-2 +3-719 11 and 82.379 -11 7489)