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Prove that if n2 is divisible by 4 then n^2  4 is divisible by 16.
 one year ago
 one year ago
Prove that if n2 is divisible by 4 then n^2  4 is divisible by 16.
 one year ago
 one year ago

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PhoenixFireBest ResponseYou've already chosen the best response.0
For a given integer.
 one year ago

carl51Best 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
 one year ago

zzr0ck3rBest ResponseYou've already chosen the best response.1
I would do contradiction
 one year ago

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

zzr0ck3rBest ResponseYou've already chosen the best response.1
do you need to show for all n?
 one year ago

PhoenixFireBest ResponseYou've already chosen the best response.0
I need to show the proof.
 one year ago

zzr0ck3rBest 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
 one year ago

zzr0ck3rBest ResponseYou've already chosen the best response.1
sorry direct proof was fast I think
 one year ago

PhoenixFireBest 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.
 one year ago

zzr0ck3rBest ResponseYou've already chosen the best response.1
yeah 16  (16* any integer)
 one year ago

PhoenixFireBest ResponseYou've already chosen the best response.0
Thanks for the help.
 one year ago
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