Results 1 to 2 of 2

Math Help - Compute 3^80 (mod 7)

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    21

    Compute 3^80 (mod 7)

    I cannot remember how to do these problems and they are due right after break!!!
    Compute 3 ^80 (mod7) and find all integers x such that 5x is congruent to 1 (mod 100)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    #1: Note that: 3^6 \equiv 1 \ (\text{mod } 7)

    So: \begin{aligned} \left(3^6\right)^{{\color{red} 13}} & \equiv 1^{{\color{red} 13}} & (\text{mod } 7) \\ 3^{78} & \equiv 1 & (\text{mod } 7) \end{aligned}

    Multiply both sides by the appropriate power of 3 and you'll get your result.

    #2: If (a,m) \! \not{\mid} \ b, then ax \equiv b \ (\text{mod }n) has no solutions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Compute Hom(q,q/z)
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 5th 2011, 11:52 PM
  2. Compute a sum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2010, 05:08 AM
  3. Hoe to compute this
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 5th 2010, 10:13 AM
  4. Compute E[X] and P[Y>2]
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 4th 2009, 05:00 PM
  5. compute a sum
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 7th 2006, 10:32 AM

Search Tags


/mathhelpforum @mathhelpforum