Results 1 to 2 of 2

Math Help - Arithmetic Prove

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    6

    Arithmetic Prove

    IMPORTANT: Number and explain (in english) your steps.

    Prove that, every square number has either the form 4q or 4q + 1 for some integer q.

    Use formats of sqrt(x) for √x and x^k for xk


    Added to this post by the OP after the reply by Mr F:

    I have this

    We are trying to prove the statement, x^2 = 4n or 4n + 1 for some integer n. If x is even, then x = 2k for some integer k, so x^2 = 4k^2. Setting n = k^2 gives us an integer n such that x^2 = 4n, and we are done. If x is odd, then x = 2k + 1 for some integer k. Thus, x^2 = (2k+1)^2 = 4k^2 + 4k + 1. Letting n = 4(k^2 + k), we have x^2 = (2k+1)^2 = 4n + 1. Since k is an integer, n = 4(k^2 + k) is also an integer
    Last edited by mr fantastic; April 13th 2009 at 09:02 PM. Reason: Made clear an edit has been made after getting a reply.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by smh745 View Post
    IMPORTANT: Number and explain (in english) your steps.

    Prove that, every square number has either the form 4q or 4q + 1 for some integer q.

    Use formats of sqrt(x) for √x and x^k for xk
    Step1: What have you tried?

    Spoiler:
    Steps 2 - : Note that square numbers can be generated by taking the product of two consecutive even or odd numbers and adding 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using modular arithmetic to prove divisibility
    Posted in the Discrete Math Forum
    Replies: 15
    Last Post: February 14th 2010, 12:52 PM
  2. Arithmetic Progression or Arithmetic Series Problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 8th 2009, 12:36 AM
  3. Replies: 1
    Last Post: May 22nd 2009, 10:10 AM
  4. Replies: 3
    Last Post: May 21st 2009, 11:01 PM
  5. Replies: 2
    Last Post: May 21st 2009, 09:20 PM

Search Tags


/mathhelpforum @mathhelpforum