(a) Given an integer N, let M be the integer formed by reversing the order of the digits of N (for example, if N = 6923, then M = 3296). Verify that N - M is divisible by 9.

(b) A palindrome is a number that reads the same backward as forward (for instance, 373 and 521125 are palindromes). Prove that any palindrome with an even number of digits is divisible by 11.