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2023 SSMO Relay Round 1 Problems

Problem 1

Compute the remainder when $2022^{2021^{2020^{\dots}}}$ is divided by $2023$.

Solution

Problem 2

Let $T=TNYWR$. Let $a_0 = 3, a_1 = 1, a_2 = T$, and let $a_n = a_{n-1} - \frac{a_{n-3}}{8}$ for $n \ge3.$ Find \[\sum_{i=0}^\infty a_i.\]

Solution

Problem 3

Let $T=TNYWR$. Find the number of solutions to the equation \[\sec^{T} (Tx) - \tan^{T}(Tx) = 1\] such $0 \le x \le \pi$

Solution

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