Showing that $1+2020^y$ ($y\in \mathbb{Z}$) is not a perfect square

Since $2020=673\cdot 3+1\equiv 1\pmod 3$ we have $2020^y \equiv 1^y=1\pmod 3$ for all $y\in\mathbb N$ so that $$1+2020^y\equiv 2\pmod 3,$$

but every square is equivalent to $0$ or $1$ modulo $3$ which implies that $1+2020^y$ is never a perfect square.