Category:Examples of Chinese Remainder Theorem
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This category contains examples of use of Chinese Remainder Theorem.
Let $b_1, b_2, \ldots, b_r \in \Z$.
Let $n_1, n_2, \ldots, n_r$ be pairwise coprime positive integers.
Let $\ds N = \prod_{i \mathop = 1}^r n_i$.
Then the system of linear congruences:
| \(\ds x\) | \(\equiv\) | \(\ds b_1\) | \(\ds \pmod {n_1}\) | |||||||||||
| \(\ds x\) | \(\equiv\) | \(\ds b_2\) | \(\ds \pmod {n_2}\) | |||||||||||
| \(\ds \) | \(\vdots\) | \(\ds \) | ||||||||||||
| \(\ds x\) | \(\equiv\) | \(\ds b_r\) | \(\ds \pmod {n_r}\) |
has a solution which is unique modulo $N$:
- $\exists ! a \in \Z_{>0}: x \equiv a \pmod N$
Pages in category "Examples of Chinese Remainder Theorem"
The following 2 pages are in this category, out of 2 total.