. Prove that if a E Z, then 4 {(12 + 1. 3 . Let :c be a positive real number. Prove that if a; E > 2, then :1: > 3. . Prove that if k E Z then 3|k(2k + 1)(4k + 1). . Let n E Z. a.) Show that if 3 | n and 4 | n, then 12 | n. b) Use the previous part to show that if n > 3 is a prime, then 71 (mod 12). 2: . Let n E Z. Prove that if n3 + n2 n | 3 is a multiple of three, then n is a multiple of three