## Explorations
43. Use mathematical induction to prove that 2 is a factor of (n+1)(n+2) for all positive integers n.
44. Use mathematical induction to prove that 6 is a factor of n(n+1)(n+2) for all positive integers n. (You may assume the assertion in Exercise 43 to be true.)
45. Give an alternate proof of the assertion in Exercise 43 based on the fact that (n+1)(n+2) is a product of two consecutive integers.
46. Give an alternate proof of the assertion in Exercise 44 based on the fact that n(n+1)(n+2) is a product of three consecutive integers.