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PhoenixFire
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Prove that if n2 is divisible by 4 then n^2  4 is divisible by 16.
 2 years ago
 2 years ago
PhoenixFire Group Title
Prove that if n2 is divisible by 4 then n^2  4 is divisible by 16.
 2 years ago
 2 years ago

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PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
For a given integer.
 2 years ago

carl51 Group TitleBest ResponseYou've already chosen the best response.0
Say that n is 26 so 262=24 and 24 is divisible by 4. 26x 24=524=48 and 48 is divisible by 16
 2 years ago

zzr0ck3r Group TitleBest ResponseYou've already chosen the best response.1
hehe I wish, sec
 2 years ago

zzr0ck3r Group TitleBest ResponseYou've already chosen the best response.1
I would do contradiction
 2 years ago

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

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

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
I need to show the proof.
 2 years ago

zzr0ck3r Group TitleBest ResponseYou've already chosen the best response.1
ok 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
 2 years ago

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

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.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.
 2 years ago

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

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
Thanks for the help.
 2 years ago
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