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(e) The following theorem is true, but the proof is wrong. Explain where the mistake is in the proof. Write no more than four sentences. Theorem. Suppose ne N. Then 2³n - 1 is divisible by 7. Proof. 23n = (2³)n = 8", which is divisible by 8 because n > 0. So 2³h is a multiple of 8, and therefore 23n - 1 is a multiple of 8 - 1, i.e. is a multiple of 7. [4]

(e) The following theorem is true, but the proof is wrong. Explain where the mistake is in the proof. Write no more than four sentences. Theorem. Suppose ne N. Then 2³n - 1 is divisible by 7. Proof. 23n = (2³)n = 8", which is divisible by 8 because n > 0. So 2³h is a multiple of 8, and therefore 23n - 1 is a multiple of 8 - 1, i.e. is a multiple of 7. [4]

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(e) The following theorem is true, but the proof is wrong. Explain where the mistake is in the proof. Write no more than four sentences. Theorem. Suppose n E N. Then 2³n – 1 is divisible by 7. Proof. 23n = (2³)n = 8′, which is divisible by 8 because n > 0. So 2³n is a multiple of 8, and therefore 23 - 1 is a multiple of 8 – 1, i.e. is a multiple of 7. [4]
Transcribed Image Text:(e) The following theorem is true, but the proof is wrong. Explain where the mistake is in the proof. Write no more than four sentences. Theorem. Suppose n E N. Then 2³n – 1 is divisible by 7. Proof. 23n = (2³)n = 8′, which is divisible by 8 because n > 0. So 2³n is a multiple of 8, and therefore 23 - 1 is a multiple of 8 – 1, i.e. is a multiple of 7. [4]
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