# Thread: Need help on an easy proof

1. ## Need help on an easy proof

need to prove that:
if m, d, and k are nonnegative integers and d does not equal 0, then (m + dk) mod d = m mod d.

I'm pretty sure you need to use the quotient remainder theorem.

2. $\displaystyle m + dk \mod d \equiv m \mod d + dk \mod d \equiv m \mod d + 0 \mod d \equiv m \mod d$. Is there any reason you can't use this argument?

3. how do you know (m + dk) mod d = m mod d + dk mod d?

is that a rule that works for all integers?

also

wouldn't m mod + 0 mod d = m mod d + d and not m mod d

4. Originally Posted by Mathwizard4
how do you know (m + dk) mod d = m mod d + dk mod d?

is that a rule that works for all integers?
Yes, it does. The remainder when a + b is divided by d is congruent to the sum of the remainder of a when divided by d and the remainder of b when divided by d.

wouldn't m mod + 0 mod d = m mod d + d and not m mod d ?

6. Originally Posted by Mathwizard4
wouldn't m mod + 0 mod d = m mod d + d and not m mod d
Not sure what you're asking here. Do you mean $\displaystyle m \mod (d + d)$ or $\displaystyle m \mod d + d \mod d$?

7. how do you know....

$\displaystyle m \mod d + dk \mod d \equiv m \mod d + 0 \mod d$

8. can anyone else help?