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.