Proof by Induction - Divisibility Proofs

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Homework Help Overview

The discussion revolves around a proof by induction related to divisibility, specifically aiming to show that a certain expression is divisible by 6. The original poster expresses difficulty in their attempts to demonstrate this property.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the manipulation of expressions and the correctness of using implication symbols versus equality. There are inquiries about the steps taken to rewrite the original expression and whether the rewritten form maintains equivalence.

Discussion Status

Some participants have offered guidance on the expression's manipulation and have prompted the original poster to clarify their reasoning. Multiple interpretations of the expressions are being explored, but there is no explicit consensus on the approach to take.

Contextual Notes

The original poster has referenced an attachment for the specific problem statement, which may contain additional context or constraints relevant to the proof.

odolwa99
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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.
 

Attachments

  • photo (2).jpg
    photo (2).jpg
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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?
 
May I ask how you solved for...
7*7k + 7*4k + 7 - 3*4k - 6
from
7*7k + 4*4k + 1?
 
odolwa99 said:
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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