Proof by Induction - Divisibility Proofs

  1. 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 Files:

  2. jcsd
  3. Mark44

    Staff: Mentor

    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?
     
  4. May I ask how you solved for...
    7*7k + 7*4k + 7 - 3*4k - 6
    from
    7*7k + 4*4k + 1?
     
  5. Mark44

    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.
     
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