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.

thanks in advance.

2. $m + dk \mod d \equiv m \mod d + dk \mod d \equiv m \mod d + 0 \mod d \equiv m \mod d$. 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.

5. ok thanks but what about this

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 $m \mod (d + d)$ or $m \mod d + d \mod d$?

7. how do you know....

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

8. can anyone else help?

9. answer?

sorry to hop on your thread with a question, but did you ever figure out how to prove that? I have the same exact problem and cannot figure it out at all, driving me insane and its due in about 6 hours

10. Originally Posted by discreteDilema
sorry to hop on your thread with a question, but did you ever figure out how to prove that? I have the same exact problem and cannot figure it out at all, driving me insane and its due in about 6 hours
not yet I gave up. but I don't need to have it for anything. sorry senor