# Proof by Induction - Divisibility Proofs

by odolwa99
Tags: divisibility, induction, proof, proofs
 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
 Mentor P: 19,694 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?
 P: 85 May I ask how you solved for... 7*7k + 7*4k + 7 - 3*4k - 6 from 7*7k + 4*4k + 1?
Mentor
P: 19,694

## Proof by Induction - Divisibility Proofs

 Quote by odolwa99 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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