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Remainder
Assume we want to find a % n. Let n = p1 * p2. Find a % p1 and a % p2. Call a % p1 = x1 Call a % p2 = x2; For finding a % n. We can do following. Write a % n = x1 * alpha1 + x2 * alpha2;
How to find alpha1 and alpha2 and how to prove that a % n = x1 * alpha1 + x2 * alpha2 ?
