# Math Help - CRT(chinese remainder theorem)

1. ## CRT(chinese remainder theorem)

how do we use the chinese remainder theorem
Suppose i have 2 numbers 197,1987 and i have 2 other integers 13 and 17
i want to find x which when divide by 197 and 1987 leaves 13 and 17 as remainder.how will we find it?give all the equations and working

2. check out this one http://www.mathhelpforum.com/math-he...two-digit.html

I go through the explanation of the chinese theorem in the case of the integers. That should help. You just gotta make sure the two mudulos are relatively prime, this ensures the ideals are comaximal and the group homomorphism is surjective (gcd(m,n)=1)

$\phi:\mathbb{Z} \rightarrow \frac{\mathbb{Z}}{m\mathbb{Z}}\times \frac{\mathbb{Z}}{n\mathbb{Z}}$

With kernel $mn\mathbb{Z}$

3. ## Similar problem

Hello,

I didn't want to post the entire solution as it may spoil your efforts in solving the problem. I had solved a similar problem under CRT. I have given the link below. You can adopt the same method to find the answer for your question.

http://www.mathhelpforum.com/math-he...onditions.html

Hope it helped,
MAX