Question 57
We say that a positive rational number $q$ is magnificent if there exist four positive integers $a, b, c, d$ such that
$$
q = \frac{a^{2021} + b^{2023}}{c^{2022} + d^{2024}}
$$
Is there a positive rational number that is not magnificent?
$$
q = \frac{a^{2021} + b^{2023}}{c^{2022} + d^{2024}}
$$
Is there a positive rational number that is not magnificent?