if , then

Here is what I tried but it didn't go anywhere.

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- Jun 26th 2010, 01:12 PMdwsmithMore Congruence
if , then

Here is what I tried but it didn't go anywhere.

- Jun 26th 2010, 01:32 PMundefined
- Jun 26th 2010, 01:33 PMdwsmith
- Jun 26th 2010, 01:36 PMundefined
- Jun 26th 2010, 01:38 PMdwsmith
- Jun 26th 2010, 01:49 PMundefined
I never wrote a=b. "a turning into b" is not the same as a=b, if you meant to convey this then you need to be more clear.

All we need is .

It's perhaps a little confusing since the letters overlap.

Let's rewrite the mathworld property as follows

Let (mod m) and (mod m), then

(mod m)

So here

x=b

x'=b

y=a

y'=b - Jun 26th 2010, 02:09 PMTwistedOne151An alternative
dwsmith,

An alternative, more along the lines of your original argument is take where you noted that if , then m divides a-b; and then note that if m divides a-b, it divides , so is then a multiple of m as well.

--Kevin C. - Jun 26th 2010, 02:10 PMdwsmith
- Jun 26th 2010, 02:36 PMdwsmith
Never mind, I have it.

- Jun 26th 2010, 02:48 PMundefined
I like TwistedOne151's approach, but it's good to know what kinds of rules you can apply with congruences, which can make things easier in general, for example

as long as

etc.

This will help later on; for example, using Euler's theorem, you will be able to do this manipulation:

given that gcd(a,n)=1.