1. The problem statement, all variables and given/known data Prove that is m, n, and d are integers and d divides (m-n) then m mod d = n mod d. 2. Relevant equations Quotient Remainder Theorem: Given any integer n and positive integer d, there exists unique integers q and r such that n=dq + r and 0[tex]\leq[/tex]r<d and n mod d = r. 3. The attempt at a solution Proof: Let m, n, d [tex]\in[/tex] Z st d divides (m-n) [tex]\exists[/tex] k [tex]\in[/tex] Z st m=dk + r [tex]\exists[/tex] j [tex]\in[/tex] Z st n=dj + s m-n=(dk + r)-(dj + s) =dk+r-dj+s =d(k-j)+(r-s) Am I going along with the proof correctly? I don't know where to go from this point and would really appreciate some help.