Results 1 to 5 of 5

Math Help - Divisibility (gcd) 3

  1. #1
    Sea
    Sea is offline
    Junior Member Sea's Avatar
    Joined
    Dec 2008
    From
    Turkey
    Posts
    50

    Divisibility (gcd) 3

    Show that : b\neq 0 and a=bx+cy \Rightarrow  (b,c)\leq (a,b)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by Sea View Post
    Show that : b\neq 0 and a=bx+cy \Rightarrow  (b,c)\leq (a,b)
    (b,c) | a (Why?) \Rightarrow (b,c) | (a,b) \Rightarrow (b,c) \leq (a,b)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Sea
    Sea is offline
    Junior Member Sea's Avatar
    Joined
    Dec 2008
    From
    Turkey
    Posts
    50
    I think...


    (a,b)\geq 0 , (b,c)\geq 0



     (b,c)|a \Rightarrow(b,c)|a and (b,c)|b\Rightarrow<br />
(b,c)|(a,b)\Rightarrow (b,c)\leq (a,b)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by Sea View Post
    I think...


    (a,b)\geq 0 , (b,c)\geq 0



     (b,c)|a \Rightarrow(b,c)|a and (b,c)|b\Rightarrow<br />
(b,c)|(a,b)\Rightarrow (b,c)\leq (a,b)
    Right

    Also (b,c)|a since a = bx+cy
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Sea
    Sea is offline
    Junior Member Sea's Avatar
    Joined
    Dec 2008
    From
    Turkey
    Posts
    50
    I can understand......


    Thanks a million...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Divisibility 11
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: December 20th 2008, 03:41 AM
  2. Divisibility (gcd) 10
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 19th 2008, 05:44 PM
  3. Divisibility (gcd) 9
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 19th 2008, 02:12 PM
  4. Divisibility (gcd) 8
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: December 19th 2008, 04:53 AM
  5. Divisibility
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 14th 2008, 10:24 AM

Search Tags


/mathhelpforum @mathhelpforum