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
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Chapter2: Second-order Linear Odes
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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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