Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

N^2 Modular Arithmetic

  1. Sep 3, 2008 #1
    proof:
    n^2 congruent 0 or 1 (mod3) for any integer n
     
  2. jcsd
  3. Sep 3, 2008 #2
    Try considering the two cases where n^2is either even or odd and how that relates to the congruence modulo 3.
     
  4. Sep 3, 2008 #3
    Two other methods:

    Consider just the squares of the integers from 1 to 9 modulo 3. Then you could generalize to higher numbers since powers of 10 are congruent to 1 (mod 3).

    Or, consider a number in base 3. It can end in 0, 1 or 2. Thus a square in base 3 can only end in 0^2 = 0, 1^2 = 1, or 2^2 = 4 = 1 base 3. So a square in base 3 can only end in 0 or 1, which is equivalent to the square leaving a remainder of 0 or 1 upon division by 3.
     
  5. Sep 3, 2008 #4
    Going along with what jeffreydk said, if n is an odd integer, what form does it have? what about if n is an even integer?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: N^2 Modular Arithmetic
  1. Modular arithmetic (Replies: 11)

  2. Modular arithmetic (Replies: 1)

  3. Modular arithmetic (Replies: 4)

Loading...