Results 1 to 3 of 3

Math Help - Kraitchik method

  1. #1

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2

    First, 143^2=20,449, so:

    u_1=143^2-20,437=12=2^2\cdot 3

    u_2=144^2-20,437=299

    u_3=145^2-20,437=588=2^2\cdot 3\cdot 7^2

    We see that u_1\cdot u_3=2^4\cdot 3^2\cdot 7^2 , a square, so now:

    143\cdot 145=20,735=298\!\!\!\pmod{20,437}\,,\,\,\sqrt{u_1\  cdot u_2}=2^2\cdot 3\cdot 7=84 , and since 298\neq 84\!\!\!\pmod{20,437}, we get:

    gcd(298-84\,,\,20,437)=107 , since 20,437=95\cdot 214+107\,,\,\,214=2\cdot 107

    Thus, as \frac{20,437}{107}=191, we finally get 20,437=107\cdot 191

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    24

    Thank You!

    I appreciate all the help you have been giving me!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: March 6th 2010, 03:40 AM
  2. Replies: 5
    Last Post: January 22nd 2010, 05:50 AM
  3. Replies: 2
    Last Post: August 17th 2008, 12:02 PM
  4. Replies: 3
    Last Post: November 3rd 2007, 01:43 PM
  5. Replies: 0
    Last Post: January 4th 2007, 01:29 PM

Search Tags


/mathhelpforum @mathhelpforum