Evaluation of proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) For each natural number n with n > 2, 2" > 1 + n. Proof. We let k be a natural number and assume that 2k > 1 + k. Multiplying both sides of this inequality by 2, we see that 2k+1 > 2+ 2k. However, 2 + 2k > 2 + k and, hence, 2k+1 > 1+ (k + 1). By mathematical induction, we conclude that 2" > 1+ n.

Q: 3. Prove the statement "6 divides n³ - n for all integers n> 0".

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Q: 19. Evaluation of Proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a)…

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A: see the attachments below

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Q: Number theory

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.