Problem of Chinese Remainder Theorem

Revision en1, by john_hopes, 2018-10-23 23:01:51

Suppose, I know m1, m2, m3 and P1, P2, P3 of the following equations. Here P1, P2, P3 are prime numbers.

X mod P1 = m1

X mod P2 = m2

X mod P3 = m3

Now, for another prime number P4,

I need to find, X mod P4 = ?

Using Chinese Remainder Theorem I can calculate this if P4 is not a prime and is equal to (P1xP2xP3).

How can I solve this problem for any prime P4?

Tags chinese remainder theo., modular arithmetic, #number theory


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en1 English john_hopes 2018-10-23 23:01:51 440 Initial revision (published)