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5. Show that if a|b then −a|b. 6. Prove or disprove: For any integers a,b, c,...

5. Show that if a|b then −a|b.

6. Prove or disprove: For any integers a,b, c, if a ∤ b and b ∤ c, then a ∤ c.

7. Use mathematical induction to show that, ∀n ≥ 0, 2|(3n +1)

8. Solve the following. (a) List the first four terms of the recursive sequence defined by s1 = 1 and ∀n ≥ 2, sn = (sn−1 + 1) 2 . (b) Given that ∑i=1n   (i= n(n+1)/2) , find the sum 2 + 4 + 6 +...+ 200

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