[PDF] chinese remainder theorem examples

Example: Solve the simultaneous congruences x ? 6 (mod 11), x ? 13 (mod 16), x ? 9 (mod 21), x ? 19 (mod 25). Solution: Since 11, 16, 21, and 25 are pairwise relatively prime, the Chinese Remainder Theorem tells us that there is a unique solution modulo m, where m = 11?16?21?25 = 92400.
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  • What is the formula for the Chinese remainder theorem?

    Here is a more general form of the Chinese remainder theorem. x ? a1 mod m1, x ? a2 mod m2, , x ? ar mod mr, has a solution, and this solution is uniquely determined modulo m1m2 ···mr.

  • How to solve 233 mod 105?

    x = 233.
    On further simplification we get, 23 ? 2(mod 3); 23 ? 3(mod 5); 23 ? 2(mod 7) ? 233 ? 23(mod 105) and 23 is the smallest solution.

  • What is Chinese remainder theorem powers?

    The Chinese remainder theorem is a powerful tool to find the last few digits of a power.
    The idea is to find a number mod 5 n 5^n 5n and mod 2 n , 2^n, 2n, and then combine those results, using the Chinese remainder theorem, to find that number mod 1 0 n 10^n 10n.

  • What is Chinese remainder theorem powers?

    The Chinese Remainder Theorem states assert that for pairwise coprime integers in modular congruences, there is one number x which is a solution.
    It also explores how to find that number x.
    Relatively prime - ?A synonym for the word coprime.
    Relatively prime integers do not share any factors in common other than 1.

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https://www.math.tamu.edu/~stephen.fulling/chinese.pdf