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Homework Help: Integers Module n

  1. Jun 26, 2014 #1
    1. The problem statement, all variables and given/known data
    If a I san integer, show that a^2~0 or a^2~1 in mod 4 (~ represent equivalence)

    2. Relevant equations

    3. The attempt at a solution
    my ATTEMPT:
    I started with the division algorithm..
    a = 2q + 1 for all odd numbers
    a = 2q + 0 for all even numbers
    then I squared the formula for even numbers...
    a^2 = 4q^2 + 0... but q is arbitrary so
    a^2 ~ 0 mod 4 for even numbers

    then I did the same for odd numbers
    a^2 = 4q^2 + 4q + 1
    and then I said since q was arbitrary again I could say
    a^2 = 4q + 1
    a^2~1 mod 4 for odd numbers

    is this the correct approach?
  2. jcsd
  3. Jun 26, 2014 #2
    Yep, clean work.
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