Results 1 to 7 of 7

Math Help - Modern Algebra question

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    22

    Modern Algebra question

    Evaluate modulo 5.

    [(4+6)9 + 12(124)]^101

    write as an element of the set {[0],[1],[2],[3],[4]}.

    Could someone help me please

    Would it be 1578 ^ 1
    which would be 3 modulo 5? or am I way off? Also, how would I write it as an element of the set above?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by jujab View Post
    Evaluate modulo 5.

    [(4+6)9 + 12(124)]^101

    write as an element of the set {[0],[1],[2],[3],[4]}.

    Could someone help me please

    Would it be 1578 ^ 1
    which would be 3 modulo 5? or am I way off? Also, how would I write it as an element of the set above?

    Doing arithmetic modulo 5, we get that:

    [(4+6)9 + 12(124)]^{101} = [(4+1)\cdot 4 + 2\cdot 4)^{101} = 3^{101} = (3^{20})^5\cdot 3= 3^{20}\cdot 3=(3^5)^4\cdot 3=3^4\cdot 3=... ...and now you end the argument.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    22
    So then it would be 3^4*3 => 3^5 => 3mod5 right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by jujab View Post
    So then it would be 3^4*3 => 3^5 => 3mod5 right?

    Yup

    Tonio
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2009
    Posts
    22
    Thank you Tonio!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Aug 2009
    Posts
    170
    Thanks
    8
    Or you could use Fermat's little theorem

    3^{101} \equiv 3^{100} \cdot 3 \equiv (3^{25})^4 \cdot 3 \equiv 1 \cdot 3 \equiv 3 \ (mod \ 5)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2009
    Posts
    22
    Thanks Bingk! Much cleaner!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modern Algebra Problem
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 28th 2010, 06:57 AM
  2. Modern Algebra, Groups, Integral domains, fields...
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: December 3rd 2008, 12:15 PM
  3. modern alg
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 7th 2008, 10:42 AM
  4. Modern Algebra Problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 3rd 2008, 04:19 PM
  5. [SOLVED] Hello i need help with modern algebra
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 17th 2005, 09:47 PM

Search Tags


/mathhelpforum @mathhelpforum