The remainder when $$7^{2022} + 3^{2022}$$ is divided by 5 is

We need to find the remainder when $$7^{2022} + 3^{2022}$$ is divided by 5.

To begin, we find $$7^{2022} \pmod{5}$$. Since $$7 \equiv 2 \pmod{5}$$ and the powers of 2 modulo 5 follow a cycle of length 4, namely $$2^1 \equiv 2, \quad 2^2 \equiv 4, \quad 2^3 \equiv 3, \quad 2^4 \equiv 1 \pmod{5}$$, and since $$2022 = 4 \times 505 + 2$$, it follows that $$7^{2022} \equiv 2^{2022} \equiv 2^2 \equiv 4 \pmod{5}$$.

Next, we find $$3^{2022} \pmod{5}$$. The powers of 3 modulo 5 also follow a cycle of length 4: $$3^1 \equiv 3, \quad 3^2 \equiv 4, \quad 3^3 \equiv 2, \quad 3^4 \equiv 1 \pmod{5}$$. Again, since $$2022 = 4 \times 505 + 2$$, we have $$3^{2022} \equiv 3^2 \equiv 4 \pmod{5}$$.

Adding these results gives $$7^{2022} + 3^{2022} \equiv 4 + 4 \equiv 8 \equiv 3 \pmod{5}$$.

Therefore, the remainder is 3.

The correct answer is Option C: 3