Proof by Induction - Divisibility Proofs

Click For Summary
The discussion centers on proving a divisibility statement by induction, specifically showing that a certain expression is divisible by 6. A participant expresses difficulty in their proof and seeks assistance in identifying errors. Another contributor points out incorrect usage of implication symbols and clarifies the transformation of the expression. The focus is on demonstrating that the rewritten expression maintains equality and can be factored to show divisibility by 6. The conversation emphasizes the importance of correctly manipulating algebraic expressions in proofs.
odolwa99
Messages
85
Reaction score
0

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
    22.3 KB · Views: 625
Physics news on Phys.org
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.
 

Similar threads

Proof of Inequality: Induction & Derivation Help
  • · Replies 12 ·
Replies
12
Views
2K
Proof via mathematical induction
  • · Replies 17 ·
Replies
17
Views
2K
Prove that the product of any three consecutive integers is
  • · Replies 11 ·
Replies
11
Views
3K
Induction Proof for A^n = 1 2^nProve your formula by mathematical induction.
  • · Replies 31 ·
2
Replies
31
Views
3K
Prove ##5^n+9<6^n## for ##n\epsilon N|n\ge2## by induction
  • · Replies 5 ·
Replies
5
Views
3K
Upper & Lower Bounds Real Zeros-Polynomial Division, Proofs?
  • · Replies 4 ·
Replies
4
Views
4K
Help with an arithmetic proof by induction
  • · Replies 4 ·
Replies
4
Views
2K
Prove that {x∈ℤ : 2|x} ∩ {x∈ℤ : 9|x} ⊂ {x∈ℤ : 6|x}
  • · Replies 17 ·
Replies
17
Views
3K
Prove that the product of 4 consecutive numbers cannot be a perfect square
  • · Replies 14 ·
Replies
14
Views
4K
Is This Proof That 8 Divides n^2 - 1 for Odd n Valid?
  • · Replies 11 ·
Replies
11
Views
5K