A community for students.
Here's the question you clicked on:
 0 viewing
PhoenixFire
 3 years ago
Prove that if n2 is divisible by 4 then n^2  4 is divisible by 16.
PhoenixFire
 3 years ago
Prove that if n2 is divisible by 4 then n^2  4 is divisible by 16.

This Question is Closed

PhoenixFire
 3 years ago
Best ResponseYou've already chosen the best response.0For a given integer.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Say that n is 26 so 262=24 and 24 is divisible by 4. 26x 24=524=48 and 48 is divisible by 16

zzr0ck3r
 3 years ago
Best ResponseYou've already chosen the best response.1I would do contradiction

PhoenixFire
 3 years ago
Best ResponseYou've already chosen the best response.0\[\forall{n}\in \mathbb{Z} : 4n2 \rightarrow 16n^24\] I believe that's the correct notation.

zzr0ck3r
 3 years ago
Best ResponseYou've already chosen the best response.1do you need to show for all n?

PhoenixFire
 3 years ago
Best ResponseYou've already chosen the best response.0I need to show the proof.

zzr0ck3r
 3 years ago
Best ResponseYou've already chosen the best response.1ok assume n2= 4k for some k in Z then n = 4k+2 then n^24 = (4k+2)^2  4 = 16k^2 + 16k +44 = 16(k^2+k) since k^2+k is in Z 16n^24

zzr0ck3r
 3 years ago
Best ResponseYou've already chosen the best response.1sorry direct proof was fast I think

PhoenixFire
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah, 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.

zzr0ck3r
 3 years ago
Best ResponseYou've already chosen the best response.1yeah 16  (16* any integer)

PhoenixFire
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks for the help.
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.