5. In this question you will prove that 3 is irrational.

(a) Let n be an integer. Prove that if 3|n 2 then 3|n. Hint: consider the contrapositive and consider cases.

(b) Following the proof that 2 is irrational, use the result you have just shown above to prove that 3 is also irrational.

6. Let x be a real number such that x > 0. Prove that x + 1 4x 1.

7. Prove that it is impossible to find integers x, y such that 2x + 6 = 8y + 5.