Question 161
Let $a$ be the positive root of equation $x + \frac{1}{x} = 675$. Prove that
$$
\varphi(2023(a^{2^n} + a^{-2^n})) \gt 2 \cdot \varphi(2022(a^{2^n} + a^{-2^n}))
$$
for all $n \in \mathbb{Z}^+$.
$$
\varphi(2023(a^{2^n} + a^{-2^n})) \gt 2 \cdot \varphi(2022(a^{2^n} + a^{-2^n}))
$$
for all $n \in \mathbb{Z}^+$.