olympiads

mod{n+1} \] Replace \( n \equiv -1 \pmod{n+1} \): 3. \[ (-1)^2 + 2 = 1 + 2 = 3 \] For \( n + 1 \) to divide \( n^2 + 2 \), it must divide 3. 4. Therefore, \( n + 1 \in \{1, 3\} \), which gives \( n = 0 \) (not positive) or \( n = 2 \). 5. Final

hinder future learning. 2. Enhancing Problem-Solving Skills Olympiad-level questions are often challenging and require analytical thinking. Regular practice sharpens these skills early on. 3. Increased Confiden