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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?
Just find X from the three equations, and calculate X mod P4? I assume it's given to you.
how can I find the smallest x from here? can you explain a lil bit?
If P4 is different from P1, P2 and P3, then (by the Chinese Remainder Theorem) X mod P4 can be anything, as you can solve the 4-equation system regardless of the value you choose for X mod P4.