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

Homework Help: Algebra question

  1. Feb 10, 2009 #1

    tgt

    User Avatar

    1. The problem statement, all variables and given/known data
    Does R/Z under addition has an infinite number of elements of order 4? Where R denotes the real numbers and Z denotes the integers.






    3. The attempt at a solution
    Yes. Consider the cosets p/4+Z for primes p greater than 2. Since there are an infinite number of primes, there are an infinite number of such cosets. But the answer says no for this question.
     
  2. jcsd
  3. Feb 10, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    But each prime > 2 is 1 or 3 modulo 4. So if p is a prime, then the coset [p/4] = p/4 + Z is either equal to [1/4] or [3/4], isn't it?
     
  4. Feb 15, 2009 #3

    tgt

    User Avatar

    Nice one.
     
  5. Feb 15, 2009 #4

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Thanks. I'll leave it to you to prove that all other examples fail as well :smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook