1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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: Number proof

  1. Jun 2, 2009 #1
    1. The problem statement, all variables and given/known data

    I need to prove that if b is coprime to 6, then b^2 is congruent to 1 (mod 24)

    2. Relevant equations

    3. The attempt at a solution

    I know that this means the gcd(b,6)=1

    Any help though to start this question off would be great thanks.
  2. jcsd
  3. Jun 2, 2009 #2


    User Avatar
    Science Advisor

    And gcd(b, 6)= 1 means b must not have 2 or 3 as factors.
  4. Jun 2, 2009 #3
    If gcd(b,6) = 1 then b = r (mod 6) for only two values of r between 0 and 5. Then we can write b = 6*n + r for some integer n and look at the expansion of (6*n + r)^2.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook