To simplify the expression t = 2^2020 - 2^2019 - 2^2018 - ... - 2 - 1, we can rewrite it as a geometric series.

The sum of a geometric series can be calculated using the formula:

S = a * (r^n - 1) / (r - 1)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term a = 2^2020, the common ratio r = 1/2, and the number of terms n = 2020.

Using the formula, we can calculate the sum of the series:

S = 2^2020 * (1/2^2020 - 1) / (1/2 - 1)
= 2^2020 * (1 - 1/2^2020) / (1/2)
= 2^2020 * (2^2020 - 1) / (1/2)
= 2^2020 * (2^2020 - 1) * 2
= 2^2022 * (2^2020 - 1)

Now, we can calculate 2021^t:

2021^t = 2021^(2^2022 * (2^2020 - 1))

Since the exponent is very large, it is not feasible to calculate it directly. However, we can simplify it further by using modular arithmetic.

Let's take the modulus of both sides with respect to a large prime number p:

2021^t ≡ x (mod p)

Now, we can calculate x using modular exponentiation:

x = (2021^(2^2022 * (2^2020 - 1))) % p

This will give us the remainder when 2021^t is divided by p.