# Proof by Induction - Divisibility Proofs

1. Sep 20, 2011

### odolwa99

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.

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2. Sep 20, 2011

### Staff: Mentor

You are using implication symbols (==>) incorrectly. Most of the places you have them, you should be using "=".

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?

3. Sep 20, 2011

### odolwa99

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

4. Sep 20, 2011

### Staff: Mentor

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.

Prove $5^n+9<6^n$ for $n\epsilon N|n\ge2$ by induction Jun 9, 2017