Chinese Remainder Theorem/Examples
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Examples of use of Chinese Remainder Theorem
Example: $x \equiv 2 \pmod 3, 3 \pmod 5, 2 \pmod 7$
Consider the system of simultaneous linear congruences:
\(\ds x\) | \(\equiv\) | \(\ds 2\) | \(\ds \pmod 3\) | |||||||||||
\(\ds x\) | \(\equiv\) | \(\ds 3\) | \(\ds \pmod 5\) | |||||||||||
\(\ds x\) | \(\equiv\) | \(\ds 2\) | \(\ds \pmod 7\) |
Then $x \equiv 23 \pmod {105}$