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Q3. Let k be a positive integer. Prove that ged(k, 2" + 3" +6" - 11)=1 for every %3! integer n 2 2 if and only if k = 1. Hint: Show that every prime must divide 2" +3" +6" you can choose n so to use Corollary to Fermat's little Theorem. -11 for some integer n > 2. Think how

Q3. Let k be a positive integer. Prove that ged(k, 2" + 3" +6" - 11)=1 for every %3! integer n 2 2 if and only if k = 1. Hint: Show that every prime must divide 2" +3" +6" you can choose n so to use Corollary to Fermat's little Theorem. -11 for some integer n > 2. Think how

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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Let k be a positive integer. Prove that ged(k, 2" +3" +6" 11) 1 for every Q3. integer n 2 2 if and only if k =1. %3D Hint: Show that every prime must divide 2" +3" +6" - 1 for some integer n 2 2. Think how you can choose n so to use Corollary to Fermat's little Theorem.
Transcribed Image Text:Let k be a positive integer. Prove that ged(k, 2" +3" +6" 11) 1 for every Q3. integer n 2 2 if and only if k =1. %3D Hint: Show that every prime must divide 2" +3" +6" - 1 for some integer n 2 2. Think how you can choose n so to use Corollary to Fermat's little Theorem.
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