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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F802c7fc0-acbc-4d2f-b149-6a1bdd3b3a4b%2Feff25037-1485-4d8a-a90b-568b26803878%2Fxou8j8p_processed.jpeg&w=3840&q=75)
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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