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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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  1. wio Group Title
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    Remains? Remainder?

    • 2 years ago
  2. frx Group Title
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    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
  3. ktnguyen1 Group Title
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    all I number it present as this a/3 and a can be (0,1,2,3...n)

    • 2 years ago
  4. frx Group Title
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    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 3|m then n = m -> m^2 n= (m+1) -> m^2+2m+1 n= (m+2) -> m^2+4m+2 since 3|m then 3|m^2+2m+1 and 3|m^2+4m+2 so every integer should be devisible by 3, am I on the right track?

    • 2 years ago
  5. ktnguyen1 Group Title
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    yes you got it by the way (m+2)^2=m^2+4m+4

    • 2 years ago
  6. frx Group Title
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    Great! Oh, of course it's, my bad ;)

    • 2 years ago
  7. wio Group Title
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    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
  8. ktnguyen1 Group Title
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    We did answer the remain will be all Interger #

    • 2 years ago
  9. frx Group Title
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    Then you divide n^2/3, which remainders can be left over like the remainder in the euclidean algorithm

    • 2 years ago
  10. wio Group Title
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    Well you can only get remainders of 0, 1, and 2... that's obvious.

    • 2 years ago
  11. frx Group Title
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    What about the 4 I got above when n= (m+2) -> m^2+4m+4 ?

    • 2 years ago
  12. frx Group Title
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    @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
  13. ktnguyen1 Group Title
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    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
  14. frx Group Title
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    Okey I get it, thanks a lot! :)

    • 2 years ago
  15. wio Group Title
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    @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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