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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.

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

carl51
 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.
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