(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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 51E
Related questions
Question
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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2Ffef1fec4-3b9f-4174-9f3e-23032289eba5%2F6faru9q_processed.png&w=3840&q=75)
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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