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Proof by Induction  Divisibility Proofs 
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#1
Sep2011, 12:50 PM

P: 85

1. The problem statement, all variables and given/known data
Q. Prove by induction that... (please see attachment). 2. Relevant equations 3. The attempt at a solution The end result should be divisible by 6, but hasn't worked out for me. Can someone help me spot where I've gone wrong? Thank you. 


#2
Sep2011, 01:15 PM

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P: 21,258

You are using implication symbols (==>) incorrectly. Most of the places you have them, you should be using "=".
As to your question, 7*7^{k} + 4*4^{k} + 1 = 7*7^{k} + 7*4^{k} + 7  3*4^{k}  6. Can you show that the expression above has a factor of 6 in it? 


#3
Sep2011, 01:43 PM

P: 85

May I ask how you solved for...
7*7k + 7*4k + 7  3*4k  6 from 7*7k + 4*4k + 1? 


#4
Sep2011, 01:52 PM

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P: 21,258

Proof by Induction  Divisibility Proofs



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