1) In this problem, you may use the fact (which we will prove inChapter 6) that an integer n is not divisible by 3 if and only ifthere exists an integer k such that n = 3k + 1 or n = 3k + 2.
(a) Prove that for all integers n, if 3 | n2, then 3 | n.
2) Let a and b be positive integers. Prove that if a | b and b |a, then a = b.
3) Determine whether each statement is true or false. If true,then prove it. If false, then provide a counterexample.
(a) The sum of two irrational numbers is irrational.
(c) The product of a nonzero rational number and an irrationalnumber is irrational.
