a) Show that n(2n + 1)(7n + 1) is divisible by 6 for all integers n. b) Find all integers n such that n(2n + 1)(7n + 1) is divisible by 12.

Explain your answer please!

(a) Remember that to prove that a number is divisible by 6, you just have to prove that it is divisible by 2 and 3.

(b) The solultions are n = 2 and 7 (mod 12).