(a) Let n E Z. Use the quotient remainder theorem to prove that if 3 { n, then either n = 3k + 1 or n = 3/ + 2 for some integer k. (Hint: recall the...

I need help on number 1. I'm not sure how to start it.

1. (a) Let n E Z. Use the quotient remainder theorem to prove that if 3 { n, then either n = 3k + 1 orn = 3/ + 2 for some integer k. (Hint: recall the fact that din if and only if the remainder n mod dis zero.)(b) Let n E Z. Use a proof by contraposition (i.e., prove the contrapositive) to show that if 3|n, then3n. (Hint: square out n = 3k + 1, n = 3/ + 2, and note that these squares are have positiveremainders, i.e., are not multiples of 3.)(c) Use a proof by contradiction to prove that 3 is irrational using the same method we did for v2.