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Found problems: 1

2018 Saudi Arabia IMO TST, 1
Denote $S$ as the set of prime divisors of all integers of form $2^{n^2+1} - 3^n, n \in Z^+$. Prove that $S$ and $P-S$ both contain infinitely many elements (where $P$ is set of prime numbers).
divisor theory prime prime divisor modular arithmetic number theory prime numbers quadratic residues