A problem I came up with on Chinese New Year

We have to solve the congruence $x^{2018} \equiv 216 \mod x - 216$ . Notice that $x^{2018} - 216^{2018}$ is divisible by $x - 216$ by the difference of powers formula so we can add it or subtract it without changing anything. If we subtract it we get the congruence $216^{2018} \equiv 216 \mod x - 216$ and equivalently, $216^{2018} - 216 \equiv 0 \mod x - 216$ . It is obvious that $x = 216^{2018}$ works and no bigger $x$ can work because if $x > 216^{2018}$ then $x - 216 > 216^{2018} - 216$ , making divisibility impossible. Thus we have deduced that $x = 216^{2018}$ .