Finding a Remainder

Date: 09/21/2007 at 10:26:56
From: Athena
Subject: how to calculate the remainder when the dividend is unknown

When the even integer n is divided by 7, the remainder is 3.  Then the 
question is what is the remainder when n is divided by 14?

Is there a common method to get the answer when the dividend is
unknown?  Honestly, I totally have no idea how to solve this kind of
question.

Date: 09/21/2007 at 12:06:13
From: Doctor Ian
Subject: Re: how to calculate the remainder when the dividend is unknown

Hi Athena,

Sometimes the place to start is with some concrete examples, just to
help you see what's going on.  What numbers, if divided by 7, leave a
remainder of 3?

  10, 17, 24, 31, 38, 45, 52, ...   

I just start with the first one (10), and count by 7.  Now, we're only
interested in the even ones, 

  10, 24, 38, 52, 66, ...

so we can start from 10 and count by 14.  Now, this is kind of
interesting, because each of these numbers is 

  10 + 14*k

for k = 1, 2, 3, ..., right?  So if you divide by 14, what remainder
will you get?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/