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  3. 1) in this problem, you may use the fact (which we

1) In this problem, you may use the fact (which we will prove in Chapter 6)...

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Advance Math

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.

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