Results 1 to 2 of 2

Math Help - Division table modulo 5

  1. #1
    Member
    Joined
    Jul 2009
    Posts
    111
    Thanks
    1

    Lightbulb Division table modulo 5

    Hi,

    I was actually looking for some notes regarding the history of the Chinese Remainder theorem and came across the link

    Chinese Remainder Theorem where they illustrate a solution which involves division table modulo 5. I quote the problem here,

    p1: x = 2 (mod 3)
    p2: x = 3 (mod 5)
    p3: x = 2 (mod 7)

    From p1, x = 3t + 2, for some integer t. Substituting this into p2 gives 3t = 1 (mod 5).
    Looking up 1/3 in the division table modulo 5, this reduces to a simpler equation

    p4: t = 2 (mod 5)
    I'm not able to follow how the '1/3' gives way to t = 2 mod 5. I tried looking for the division table modulo 5 in the web but couldn't find anything substantial.

    Can anyone shed some more light on this table?

    Thanks,
    Max
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Hi,
    Quote Originally Posted by MAX09 View Post
    From p1, x = 3t + 2, for some integer t. Substituting this into p2 gives 3t = 1 (mod 5).
    Looking up 1/3 in the division table modulo 5, this reduces to a simpler equation

    p4: t = 2 (mod 5)
    I'm not able to follow how the '1/3' gives way to t = 2 mod 5. I tried looking for the division table modulo 5 in the web but couldn't find anything substantial.
    '1/3' denotes an inverse of 3 modulo 5, that is to say a number n such that n\times 3\equiv 1 \pmod{5}. As 2\times 3=6\equiv 1\pmod{5}, 2 is an inverse of 3 modulo 5. Now if we multiply both sides of
    3\times t \equiv 1 \pmod{5}
    by 2 we get
    2\times3\times t \equiv 2 \pmod{5}
    that is to say
    t \equiv 2 \pmod{5}
    since 2\times 3\equiv 1\pmod{5}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. modulo division with negative power ?
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: January 5th 2012, 04:42 AM
  2. Modulo of squares = modulo of roots
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: December 1st 2009, 10:04 AM
  3. Polynomial division vs synthetic division
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 9th 2009, 06:49 AM
  4. Long division and table of integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2009, 10:18 PM
  5. table salt + table sugar
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: September 9th 2007, 09:35 AM

Search Tags


/mathhelpforum @mathhelpforum