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Difference between revisions of "2023 SSMO Relay Round 1 Problems"

(Created page with "==Problem 1== Compute the remainder when <math>2022^{2021^{2020^{\dots}}}</math> is divided by <math>2023</math>. Solution ==P...")
 
Line 12: Line 12:
  
 
Let <math>T=</math> TNYWR. Find the number of solutions to the equation  
 
Let <math>T=</math> TNYWR. Find the number of solutions to the equation  
−
\[
+
<cmath>\sec^{N} (Nx) - \tan^{N}(Nx) = 1</cmath>
−
    \sec^{N} (Nx) - \tan^{N}(Nx) = 1
 
−
\]
 
 
such <math>0 \le x \le \pi</math>
 
such <math>0 \le x \le \pi</math>
 
[[2023 SSMO Relay Round 1 Problems/Problem 3|Solution]]
 
[[2023 SSMO Relay Round 1 Problems/Problem 3|Solution]]

Revision as of 21:32, 15 December 2023

Problem 1

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

Solution

Problem 2

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

Solution

Problem 3

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

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