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Divisor proof with absolute values

  1. Oct 21, 2008 #1
    1. The problem statement, all variables and given/known data
    I reduced a much harder problem to the following:
    Prove that if abs(a-b) is divisible by k, and if abs(b-c) is divisible by k, then abs(a-c) is divisible by k.

    2. Relevant equations

    none really.

    3. The attempt at a solution

    I tried setting abs(a-b)/k = n and abs(b-c)/k = m where m and n are integers and trying to construct abs(a-c) from that but to no avail.
    By the definition of absolute value, I know abs(x) = x when x>0 and =-x when x<0. I think trying all of the four possible cases might work, but would there be an easier way?
    Last edited: Oct 21, 2008
  2. jcsd
  3. Oct 22, 2008 #2
    How do you get rid of the absolute values? If |x| is divisible by k, is x divisible by k?
  4. Oct 22, 2008 #3


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    Staff Emeritus
    Science Advisor

    (a- b)+ (b-c)= a- c.
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