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Simple Proof, Number Theory

  1. Mar 21, 2010 #1
    1. The problem statement, all variables and given/known data

    Use direct proof to prove "The product of any two even integers is a multiple of 4."

    2. Relevant equations

    definition of even is n=2k

    3. The attempt at a solution

    My proof is going in circles/getting nowhere.

    So far I have (shortened): By definition even n=2k, n=2j for some integer k
    2k(2j) = 4kj = 4(kj) kj is an integer because k and j are integers
    and the product of two integers is an integer
    Not sure where to take it from there or if I even set the proof up correctly!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 21, 2010 #2

    Mark44

    Staff: Mentor

    You have the gist of it, but you should use different letters for the two even integers, say m and n.

    m = 2k, and n = 2j, for integers k an j
    mk = (2k)(2j) = 4kj, which is obviously a multiple of 4.
     
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