Chinese Remainder Theorem/Examples

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 $x \equiv 23 \pmod {105}$