Results 1 to 2 of 2

Math Help - sum of 4 squares

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    55

    Post sum of 4 squares

    If 8l(x^2+y^2+z^2+w^2), show that x,y,z,w are even.
    I know I have to classify squares mod 8, but can someone show me how.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Sally_Math View Post
    If 8l(x^2+y^2+z^2+w^2), show that x,y,z,w are even.
    I know I have to classify squares mod 8, but can someone show me how.
    If a is even then a=4k+1 or a=4k+3. Notice (4k+1)^2 = 16k^2 + 8k + 1 = 8(2k^2+k) + 1. Also (4k+3)^2 = 16k^2 + 24k + 9 = 8(2k^2+3k+1)+1. Therefore, an odd integer modulo 8 is congruent to 1. Therefore, x^2+y^2+z^2+w^2 \equiv 1,2,3,4 (\bmod 8) if at least one of them is odd. Thus, we require all four to be even.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sum of squares
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 16th 2010, 07:25 PM
  2. Magic squares of Squares
    Posted in the Math Puzzles Forum
    Replies: 5
    Last Post: September 22nd 2010, 10:58 AM
  3. Squares
    Posted in the Math Puzzles Forum
    Replies: 6
    Last Post: December 2nd 2009, 07:55 PM
  4. Replies: 4
    Last Post: November 13th 2009, 06:12 PM
  5. sum of squares
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 7th 2007, 08:19 AM

Search Tags


/mathhelpforum @mathhelpforum