5. (a) Prove that Vn E N, 11 | (102+1 + 1). (b) Prove that Vn E N. 11 | (1020 - 1). (c) Given a natural number n, we can write the decimal representation of n as dedk_idk 2 ...didowhere di is the it digit and is a natural number from 0 to 9 inclusive, de * 0 for n > 0,k > 0 and: n = dy . 10" + dx_1 - 10*-14 d* 2. 10* 2 4 - -. + d . 10' + do - 10 Define the alternating sum an = do - di + de - d3 + ... + - doit ...dk- For example, 9180928 =8-249-048-1 Prove that if an is divisible by 11 then n is divisible by 11. Hint: Use what you proved in parts (a) and (b)