Results 1 to 2 of 2

Math Help - Prove their own multiplicative inverses

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    84

    Prove their own multiplicative inverses

    Let p be a prime integer. Prove that [1] and [p-1] are the only elements in Zp that are their own multiplicative inverses.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    394
    Quote Originally Posted by rainyice View Post
    Let p be a prime integer. Prove that [1] and [p-1] are the only elements in Zp that are their own multiplicative inverses.
    Hint: If x^2 \equiv 1 mod (p), then x \equiv +1 or x \equiv -1.
    U_p=\{[1], [2], \cdots ,[p-1]\} for a prime number p > 2 and U_2=\{1\}, where U_p is the group of units in \mathbb{Z}_p.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: June 15th 2011, 08:14 PM
  2. Replies: 2
    Last Post: March 8th 2010, 05:25 PM
  3. Multiplicative inverses in field extensions
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 18th 2010, 08:10 PM
  4. MOre Multiplicative inverses
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 29th 2009, 09:12 PM
  5. Multiplicative Inverses
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 19th 2008, 05:46 AM

Search Tags


/mathhelpforum @mathhelpforum