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Foundation of maths

  1. Sep 21, 2014 #1
    1. The problem statement, all variables and given/known data
    If m; n, and d are integers, d > 0, and dl(m - n), what is the relation between
    m mod d and n mod d? Prove your answer.
    2. Relevant equations
    @@@
    3. The attempt at a solution
    (m-n)/=dk >>>>>(m-n)/d=k.....equation 1
    m mod d means m=dq1+r1 where q1 is the quotient and r1 is the answer for mod
    n mod d means n=dq2+r2 where q2 is the quotient and r2 is the answer for mod

    r1-r2= m-dq1-n+dq2 =(m-n)+d(q1-q2)
    sub equation 1 into it,
    (r1-r2)/d +q1-q2=k

    how can i show that q1-q2 is equal to k so that i can conclude r1 and r2 is same. Any1?or any better solution?
     
  2. jcsd
  3. Sep 21, 2014 #2
    You want only natural number solutions, so use only multiplication and addition of variables in your algebra steps. (Do not do divisions that could create fractions.)

    With the given information, ##d | (m-n)##, write this out just like your other equations. Also, you can always replace an expression with a new variable, so ##q_1 - q_2 = q##. My recommendation is that you read the equations you create in terms of divisibility and see if you get it. "m minus n divided by d leaves a remainder of"?
     
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