Final answer:
If m, n, and d are integers, with d > 0 and d dividing (m-n), then m mod d equals n mod d because division by d leaves the same remainder for both m and n.
Step-by-step explanation:
If m, n, and d are integers, d > 0, and d | (m-n), this means d divides the difference between m and n without leaving a remainder. The question asks about the relationship between m mod d and n mod d. By definition, m mod d is the remainder when m is divided by d, and n mod d is the remainder when n is divided by d.
Since d divides (m-n), we know that (m - n) = d × k for some integer k. Therefore, when both m and n are divided by d, the remainders must be the same, implying that m mod d = n mod d.
Here's an example to illustrate the point: Let's say m = 14, n = 8, and d = 3. Since 14 - 8 = 6 and 6 is divisible by 3, we can check that 14 mod 3 = 2, and 8 mod 3 = 2, which confirms that m mod d = n mod d.