Divisible by 19!!!

Repunit is a string of $1$ 's and can be expressed as

$\frac{10^N-1}{9}$

and $N$ will be the number of digits of $1$ .

By Fermat's Little Theorem,

$10^{18}\equiv1 \mod19$

$10^{18}-1\equiv0 \mod19$

Hence, the number of digits of the number is $18$ .

I applied divisibility of 19 which states 2times times the last digit +other digits if divisible by 19 the number is divisible by 19 so 2*1+x =19 since x is 17 the number of digits is x+1=18