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frx
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Which remains can occur when dividing \[n^2\] with 3, let \[n \in \mathbb{N} \]
 2 years ago
 2 years ago
frx Group Title
Which remains can occur when dividing \[n^2\] with 3, let \[n \in \mathbb{N} \]
 2 years ago
 2 years ago

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wio Group TitleBest ResponseYou've already chosen the best response.0
Remains? Remainder?
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Sorry some difficulities with the language. What i mean is if you divide for example 4 with 3 you get the remainder 1..
 2 years ago

ktnguyen1 Group TitleBest ResponseYou've already chosen the best response.1
all I number it present as this a/3 and a can be (0,1,2,3...n)
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Ok I think i get what you say but what if I want to be more general. Let's say that n is an interger which can be written on the form m, m+1,m+2..., where 3m then n = m > m^2 n= (m+1) > m^2+2m+1 n= (m+2) > m^2+4m+2 since 3m then 3m^2+2m+1 and 3m^2+4m+2 so every integer should be devisible by 3, am I on the right track?
 2 years ago

ktnguyen1 Group TitleBest ResponseYou've already chosen the best response.1
yes you got it by the way (m+2)^2=m^2+4m+4
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Great! Oh, of course it's, my bad ;)
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Sorry, but it's still not a clear question. You want the remainder of n^2 / 3 in terms of the remainder of n/3?
 2 years ago

ktnguyen1 Group TitleBest ResponseYou've already chosen the best response.1
We did answer the remain will be all Interger #
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Then you divide n^2/3, which remainders can be left over like the remainder in the euclidean algorithm
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Well you can only get remainders of 0, 1, and 2... that's obvious.
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
What about the 4 I got above when n= (m+2) > m^2+4m+4 ?
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
@wio could you please explain why the remainders only can be 0,1,2 and why it's so obvious, would really appreciate it :)
 2 years ago

ktnguyen1 Group TitleBest ResponseYou've already chosen the best response.1
the 4 because I mean n=(m+2) but we have to find n^2 mean (m+2)^2= m^2+4m+4 I just want to corrct the formula you typed previous
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Okey I get it, thanks a lot! :)
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
@frx If you have some number, 3m+4, then you have 3m+3+1, which is 3(m+1) + 1... remainder 1!
 2 years ago
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