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(a) While the claim was incorrect, the purported proof seemingly does have some legitimate mathematical ideas. Can you revise the claim, and adapt the purported proof to obtain a correct proof of your updated claim? (b) Given your claim and proof in (a), can you come up with another result of the form "For every n N where [some condition], [some expression involving n] is not a prime and prove it? (This is obviously an open-ended, explorative question that has no set correct answer.)

(a) While the claim was incorrect, the purported proof seemingly does have some legitimate mathematical ideas. Can you revise the claim, and adapt the purported proof to obtain a correct proof of your updated claim? (b) Given your claim and proof in (a), can you come up with another result of the form "For every n N where [some condition], [some expression involving n] is not a prime and prove it? (This is obviously an open-ended, explorative question that has no set correct answer.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Claim: For every n € N, n² – 1 is not a prime number. Purported Proof: Notice that n² – 1 can be factored as (n + 1)(n − 1). Thus, n² – 1 is a product and has divisors n+ 1 and n − 1, and therefore it is not prime.
Transcribed Image Text:Claim: For every n € N, n² – 1 is not a prime number. Purported Proof: Notice that n² – 1 can be factored as (n + 1)(n − 1). Thus, n² – 1 is a product and has divisors n+ 1 and n − 1, and therefore it is not prime.
(a) While the claim was incorrect, the purported proof seemingly does have some legitimate mathematical ideas. Can you revise the claim, and adapt the purported proof to obtain a correct proof of your updated claim? (b) Given your claim and proof in (a), can you come up with another result of the form "For every n N where [some condition], [some expression involving n] is not a prime and prove it? (This is obviously an open-ended, explorative question that has no set correct answer.)
Transcribed Image Text:(a) While the claim was incorrect, the purported proof seemingly does have some legitimate mathematical ideas. Can you revise the claim, and adapt the purported proof to obtain a correct proof of your updated claim? (b) Given your claim and proof in (a), can you come up with another result of the form "For every n N where [some condition], [some expression involving n] is not a prime and prove it? (This is obviously an open-ended, explorative question that has no set correct answer.)
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Step 1: Define Prime Number

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