Proof by Induction - Divisibility Proofs


by odolwa99
Tags: divisibility, induction, proof, proofs
odolwa99
odolwa99 is offline
#1
Sep20-11, 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.
Attached Thumbnails
photo (2).jpg  
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Mark44
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#2
Sep20-11, 01:15 PM
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P: 21,073
You are using implication symbols (==>) incorrectly. Most of the places you have them, you should be using "=".

As to your question,
7*7k + 4*4k + 1
= 7*7k + 7*4k + 7 - 3*4k - 6.

Can you show that the expression above has a factor of 6 in it?
odolwa99
odolwa99 is offline
#3
Sep20-11, 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?

Mark44
Mark44 is offline
#4
Sep20-11, 01:52 PM
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P: 21,073

Proof by Induction - Divisibility Proofs


Quote Quote by odolwa99 View Post
May I ask how you solved for...
7*7k + 7*4k + 7 - 3*4k - 6
from
7*7k + 4*4k + 1?
I didn't "solve" for it; I just rewrote the second expression in a different way. You should convince yourself that the two expressions are equal.


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