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Proof: Quotient and Remainder involving floor function

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that if a (is in) Z and d (is in) Z+, d>1 then the quotient and remainder when a is divided by d are a/d and a-d(floor function(a/d))

    2. Relevant equations



    3. The attempt at a solution

    solution (that i have from handout - that i don't understand)

    by thm 2 p202 (? i am not sure what it says as it is in handwriting, but it looks like p202) we know a = dq+r 0<=r<d dividing the equation by d we have a/d = q + r/d w/ 0<=r/d<1, hence by definition it's clear q is (floor function(a/d)) while the original equation shows r = a-dq giving the second result..
     
  2. jcsd
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