Chinese remainder theorem
Systems of congruences with pairwise coprime moduli always have a solution. History: 3rd to 5th century (Sunzi).
How to work it out
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The statement:
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Systems of congruences with pairwise coprime moduli always have a solution.
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Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ x \equiv a_i \pmod{n_i}\ \text{has a unique solution mod } n_1 n_2 \cdots \]x ≡ 2 (mod 3), x ≡ 3 (mod 5), x ≡ 2 (mod 7): every x up to 210 (computed)
| x | mod 3 | mod 5 | mod 7 |
|---|---|---|---|
| 23 | 2 | 3 | 2 |
| 128 | 2 | 3 | 2 |
Questions
What is the chinese remainder theorem?
Systems of congruences with pairwise coprime moduli always have a solution.