# Need help on an easy proof

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• February 23rd 2010, 06:10 PM
Mathwizard4
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.
• February 23rd 2010, 06:18 PM
icemanfan
$m + dk \mod d \equiv m \mod d + dk \mod d \equiv m \mod d + 0 \mod d \equiv m \mod d$. Is there any reason you can't use this argument?
• February 23rd 2010, 06:39 PM
Mathwizard4
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
• February 23rd 2010, 06:48 PM
icemanfan
Quote:

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.
• February 23rd 2010, 06:52 PM
Mathwizard4
ok thanks but what about this

wouldn't m mod + 0 mod d = m mod d + d and not m mod d http://www.mathhelpforum.com/math-he...c/progress.gif ?
• February 23rd 2010, 06:55 PM
icemanfan
Quote:

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 $m \mod d + d \mod d$?
• February 23rd 2010, 07:08 PM
Mathwizard4
how do you know....

$m \mod d + dk \mod d \equiv m \mod d + 0 \mod d$
• February 23rd 2010, 09:37 PM
Mathwizard4
can anyone else help?
• February 23rd 2010, 10:22 PM
discreteDilema
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
• February 23rd 2010, 10:30 PM
Mathwizard4
Quote:

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