Results 1 to 3 of 3

Math Help - show no solutions exists using table x^3mod9

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    28

    show no solutions exists using table x^3mod9

    Hi wondering if anyone can help with this question:

    Make a table of values x^3, mod 9, and show that the equation x^2 + 2y^2 = 9z^2 has no non zero integer solutions.

    My table looks like

    n mod 9 - -4 -3 -2 -1 0 1 2 3 4
    n^3mod 9 - -1 0 1 -1 0 1 -1 0 1
    2n^3mod 9 --2 0 2 -2 0 2 -2 0 2

    i can see that by adding the two rows i get 0's at 0 and +-3 but dont really know where to go from here.

    Also if i am not given the modulo to use, how do i decide which modulo to use.
    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Dec 2011
    Posts
    16

    Re: show no solutions exists using table x^3mod9

    Quote Originally Posted by MattWT View Post
    Hi wondering if anyone can help with this question:

    My table looks like

    n mod 9 - -4 -3 -2 -1 0 1 2 3 4 ?
    n^3mod 9 - -1 0 1 -1 0 1 -1 0 1 ?
    n\ mod\ 9 0 1 2 3 4 5 6 7 8
    n^3\ mod\ 9 0 1 8 0 1 8 0 1 8


    btw, are you sure you're not being asked to construct table for x^2\ mod\ 9 not x^3\ mod\ 9 ?
    Last edited by MathFan; May 23rd 2012 at 01:06 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: show no solutions exists using table x^3mod9

    You'll want to make a table for x^2 mod 9. For example,

    1^2 \equiv 1
    2^2 \equiv 4
    3^2 \equiv 0
    4^2 \equiv 7
    5^2 \equiv 7
    6^2 \equiv 0
    7^2 \equiv 4
    8^2 \equiv 1
    9^2 \equiv 0

    Assume that at least one of x,y,z is not a multiple of 3. Even then, you can't prove that using the table, for example, you could have

     1^2 + 2*7^2 \equiv 0 (mod 9)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. show that f'(c) exists
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: October 7th 2011, 08:53 AM
  2. Replies: 3
    Last Post: August 11th 2010, 03:12 AM
  3. Show that lim_ x->a+ exists and is finite.
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: March 31st 2010, 08:08 PM
  4. Show a neighborhood exists
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 20th 2009, 04:55 PM
  5. show the root exists
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 10th 2007, 04:32 PM

Search Tags


/mathhelpforum @mathhelpforum