Question: (a) [3 marks] Prove that 3 | 22n+1 +1 for all natural numbers n. (b) [5 marks] Prove that for all positive integers n,

(a) [3 marks] Prove that 3 | 22n+1 +1 for all natural

(a) [3 marks] Prove that 3 | 22n+1 +1 for all natural numbers n. (b) [5 marks] Prove that for all positive integers n, 1 3 2n-1 1 2 XX.. 4 2n 3n HINT: You will find it difficult (likely impossible) to prove this directly. Consider proving a slightly stronger statement by making a small change to the expression inside the square root. Then, re- member to use what you prove to conclude the inequality in this question.

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