Question 71
Let $a_1, a_2, \dots, a_{2023}$ be positive real numbers with
$$
a_1 + a_2^2 + a_3^3 + \dots + a_{2023}^{2023} = 2023.
$$
Show that
$$
a_1^{2023} + a_2^{2022} + \dots + a_{2022}^2 + a_{2023} \gt 1 + \frac{1}{2023}.
$$
$$
a_1 + a_2^2 + a_3^3 + \dots + a_{2023}^{2023} = 2023.
$$
Show that
$$
a_1^{2023} + a_2^{2022} + \dots + a_{2022}^2 + a_{2023} \gt 1 + \frac{1}{2023}.
$$