Which is the smallest natural number $m$ with $m> 1$ for which the following relation does not hold: $ 11 ^ {2018} \equiv 1 \pmod m $

Question

Which is the smallest natural number $m$ with $m > 1$, for which the following relation does not hold:

$$11^{2018} \equiv 1 \pmod m $$

Answer 1

HINT: For $m = 11$, it obviously does not hold. So you have only $9$ numbers to try, namely $2,3,4,5,6,7,8,9,10$.

Answer 2

after the clues that you guys give i have figured out that $m =7$ and $$11^{2018} \equiv 2 \pmod 7 $$ Is that correct?