Results 1 to 2 of 2

Math Help - Modular Help

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    26

    Modular Help

    My problem is:

    Prove that there are no integers x and y such that x^2 − 5y^2 = 2.
    Hint: consider this equation modulo 5.

    I don't get how to start this with using modulo 5.

    do I make the whole equation divisible by 5?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Traveller's Avatar
    Joined
    Sep 2010
    Posts
    162
    Consider all possibilities. x will be one of the following :

    a) 5k
    b) 5k-1
    c) 5k-2
    d) 5k+1
    e) 5k+2

    for some suitable k.

    What remainders do these leave when squared and divided by 5 ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modular Arithmetic
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 11th 2011, 12:27 PM
  2. Modular arithmetic.
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: March 10th 2011, 06:21 PM
  3. Modular Inversion
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: August 27th 2010, 10:51 PM
  4. Modular
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 1st 2009, 12:16 PM
  5. Modular help
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 5th 2007, 12:53 PM

Search Tags


/mathhelpforum @mathhelpforum