Prove the following statements by induction:

(a) For all integers \(n \geq 0\), the number \(5^{2 n}-3^{n}\) is a multiple of 11 .

(b) For any integer \(n \geq 1\), the integer \(2^{4 n-1}\) ends with an 8 .

(c) The sum of the cubes of three consecutive positive integers is always a multiple of 9 .

(d) If \(x \geq 2\) is a real number and \(n \geq 1\) is an integer, then \(x^{n} \geq n x\).

(e) If \(n \geq 3\) is an integer, then \(5^{n}>4^{n}+3^{n}+2^{n}\).