Is There a Solution for Modulus with 3 Equations?

[coolul007]

I am wondering if there is a way to solve the following:

n == a mod(m)

m == b mod(r)

n == x mod(r), I need to know x, without dealing with a gigantic number(n),

I can find a and b, as I chose m to give me predictable results.

I appreciate any insight...

 

[Berko]

Sounds like a Chinese Remainder Theorem problem. Check out the concept online or in any book on number theory.

 

[coolul007]

It doesn' seem to be Chinese Remainder...I've looked into that. If it was Chinese Remainder it would be solving for a number with known mods, I know the number but need the missing mod.

x == a mod(m)
x == b mod(r)

 

[Berko]

Ahhh, I see. Well, never mind then!