Answer:
a good question after a long time....
we're asked
[tex] {2019}^{2019} \%2020[/tex]
we can write,
[tex] {2019}^{2019} = {(2020 - 1)}^{2019} [/tex]
now apply binomial expansion,
[tex] \binom{2019}{0} {2020}^{2019} {( - 1)}^{0} + \binom{2019}{1} {2020}^{2018} {( - 1)}^{1} + \binom{2019}{2} {2020}^{2017} {( - 1)}^{2} ... \binom{2019}{1} {2020}^{1} {( - 1)}^{2018} + \binom{2019}{2019} {2020}^{0} {( - 1)}^{2019}[/tex]
if you notice, each term except Last has 2020 in it, which would get divided... so the remainder is 1
