Proof by Induction - Divisibility Proofs

[odolwa99]

Homework Statement

Q. Prove by induction that... (please see attachment).

Homework Equations

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.

 

[Mark44]

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?

 

[odolwa99]

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

 

[Mark44]

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.