Question 131
We say a prime number $p$ is “good”, if there exists a bijection $f$ from the set $\{0, 1, \dots, p-1\}$ to itself satisfying the following condition: for any pair of elements $a, b \in \{0, 1, \dots, p-1\}$, if $p \mid a^2 - b$, then $|f(a) - f(b)| \le 2024$. If no such bijection $f$ exists, we say that the prime $p$ is “bad”.
Prove that there exist infinitely many good primes, and there exist infinitely many bad primes.
Prove that there exist infinitely many good primes, and there exist infinitely many bad primes.