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SMO 2026 Senior Round 1 Question 3

SMO · SMO 2026 Senior Round 1

Question 3

Given that the minimum value of $(\tan^{-1}x)^{2048}+\left(\tan^{-1}\frac1x\right)^{2048}$ is $\frac{\pi^a}{b}$, where $a$ and $b$ are rational numbers, and $x>0$, find the value of $\log_2\left(\frac ba\right)$.
  1. 1013
  2. 2026
  3. 4084
  4. 4085
  5. None of the above