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Determine the validity of the ff. proof: Theorem: For every integer k, if k > 0 then k² + 2k+1 is composite. "Proof: Suppose k is any integer such that k> 0. If + 2k+1 is composite, then k + 2k+1 = rs for some integers r and s such that 1

Determine the validity of the ff. proof: Theorem: For every integer k, if k > 0 then k² + 2k+1 is composite. "Proof: Suppose k is any integer such that k> 0. If + 2k+1 is composite, then k + 2k+1 = rs for some integers r and s such that 1

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Determine the validity of the ff. proof: Theorem: For every integer k, if k > 0 then 2 + 2k+1 is composite. "Proof: Suppose k is any integer such that k > 0. If k? + 2k + 1 is composite, then k? + 2k+1 = rs for some integers r and s such that 1<r<k+2k+1 and 1<s<k? + 2k+1. Since 2 + 2k+1 = rs and both r and s are strictly between 1 and R+ 2k + 1, then k² + 2k+1 is not prime. Hence K+ 2k+1 is composite as was to be shown." Yes, it is valid Not valid Maybe Insufficient information to find the answer
Transcribed Image Text:Determine the validity of the ff. proof: Theorem: For every integer k, if k > 0 then 2 + 2k+1 is composite. "Proof: Suppose k is any integer such that k > 0. If k? + 2k + 1 is composite, then k? + 2k+1 = rs for some integers r and s such that 1<r<k+2k+1 and 1<s<k? + 2k+1. Since 2 + 2k+1 = rs and both r and s are strictly between 1 and R+ 2k + 1, then k² + 2k+1 is not prime. Hence K+ 2k+1 is composite as was to be shown." Yes, it is valid Not valid Maybe Insufficient information to find the answer
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