# Foundation of maths

1. Sep 21, 2014

### Unusualskill

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
2. Relevant equations
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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. Sep 21, 2014

### 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"?