Results 1 to 2 of 2

Math Help - Number theory

  1. #1
    Senior Member
    Joined
    Sep 2012
    From
    Sweden
    Posts
    250
    Thanks
    6

    Number theory

    Hi i need help with this problem.. The quest is what positive rest do i get if i divide it with 8
    7^41+17^20-6



    I should post this on number Theory section! Im sorry
    Last edited by Petrus; September 26th 2012 at 10:54 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    146

    Re: Number theory

    Let x = 7^{41}+17^{20}-6. Determine x \mod 8 ("positive rest" I assume means positive remainder).

    7 \equiv -1 \mod 8, so 7^{41} \equiv (-1)^{41} \equiv -1 \mod 8.

    17 \equiv 1 \mod 8, so 17^{20} \equiv 1^{20} \equiv 1 \mod 8.

    Thus x \equiv 7^{41}+17^{20}-6 \equiv (-1) + (1) - 6 \equiv -6 \equiv 2 \mod 8.

    Thus x leaves remainder 2 when divided by 8.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using group theory to prove results in number theory
    Posted in the Math Philosophy Forum
    Replies: 6
    Last Post: May 12th 2012, 01:34 AM
  2. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 06:09 PM
  3. Replies: 2
    Last Post: December 18th 2008, 05:28 PM
  4. Number Theory
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: July 9th 2008, 09:46 PM
  5. Number theory, prime number
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 17th 2006, 08:11 PM

Search Tags


/mathhelpforum @mathhelpforum