Consider the two equations numbered [1] and [2]:
$$\begin{aligned}
\log _ { 2021 } a & = 2022 - a \\
2021 ^ { b } & = 2022 - b
\end{aligned}$$
(a) Equation [1] has a unique solution.\\
(b) Equation [2] has a unique solution.\\
(c) There exists a solution $a$ for [1] and a solution $b$ for [2] such that $a = b$.\\
(d) There exists a solution $a$ for [1] and a solution $b$ for [2] such that $a + b$ is an integer.