Relation of m mod d and n mod d Proven

[Unusualskill]

Homework Statement

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.

Homework Equations

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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?
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[thelema418]

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"?