1.) Utilizing the Chin. Rem. Thm., find 5 consec. pos. integers such that the following conditions hold: the first is div. by 2, the 2nd is div by 3, the 3rd is div by 5, the 4th is div. by 7 and the final (the 5th) is div. by 11.

2.) Now, prove for any pos. integer n, there will exist n consecutive pos. integers a_1, a_2, ..., a_n, such that p_i | a_i for each i, where the p_i illustrates the i-th prime.