Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

PhoenixFire

  • 2 years ago

Prove that if n-2 is divisible by 4 then n^2 - 4 is divisible by 16.

  • This Question is Closed
  1. PhoenixFire
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For a given integer.

  2. carl51
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Say that n is 26 so 26-2=24 and 24 is divisible by 4. 26x 2-4=52-4=48 and 48 is divisible by 16

  3. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hehe I wish, sec

  4. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I would do contradiction

  5. PhoenixFire
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\forall{n}\in \mathbb{Z} : 4|n-2 \rightarrow 16|n^2-4\] I believe that's the correct notation.

  6. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah

  7. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you need to show for all n?

  8. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nm i c

  9. PhoenixFire
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I need to show the proof.

  10. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok assume n-2= 4k for some k in Z then n = 4k+2 then n^2-4 = (4k+2)^2 - 4 = 16k^2 + 16k +4-4 = 16(k^2+k) since k^2+k is in Z 16|n^2-4

  11. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry direct proof was fast I think

  12. PhoenixFire
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, they wanted Direct Proof. so since n^2 - 4 = 16k the (k^2+k) in 16(k^2+k) doesn't matter, the rest match. that's what was confusing me.

  13. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah 16 | (16* any integer)

  14. PhoenixFire
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks for the help.

  15. zzr0ck3r
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    np

  16. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.