# Use the construction in the proof of the Chinese remainder theorem to find all solutions to the system of congruences x -= 2 (mod 3), x -= 1 (mod 4), and x -= 3 (mod 5).

Use the construction in the proof of the Chinese remainder theorem to find all solutions to the system of congruences $x\equiv 2\left(\text{mod}3\right),x\equiv 1\left(\text{mod}4\right),\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}x\equiv 3\left(\text{mod}5\right)$.
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Step 1
Given system of congruences is,
$x\equiv 2\left(\text{mod}3\right)$
$x\equiv 1\left(\text{mod}4\right)$
$x\equiv 3\left(\text{mod}5\right)$
To find all solutions of the system by using Chines