The remainder when this determinant is divided by 5

Question

The question is find the remainder when $\begin{vmatrix} { 2014 }^{ 2014 } & { 2015 }^{ 2015 } & { 2016 }^{ 2016 } \\ { 2017 }^{ 2017 } & { 2018 }^{ 2018 } & { 2019 }^{ 2019 } \\ { 2020 }^{ 2020 } & { 2021 }^{ 2021 } & { 2022 }^{ 2022 } \end{vmatrix}$ is divided by 5. While googling, I found this answer Is there a quick way to find the remainder when this determinant is divided by $5$? but unfortunately I don't have the skill level to understand that answer. It says I'll have to use Fermat's little theorem(https://en.wikipedia.org/wiki/Fermat%27s_little_theorem) but I can't figure out how to apply it in this question.

Answer 1

First off, you can find the remainder of all the bases, using $a\equiv b \mod m\implies a^n\equiv b^n \mod m$. From there, you can show that $2015^{2015}\equiv2020^{2020}\equiv0\mod5$ and various other results. From there, you can use Fermat's Little Theorem.