Find all pairs $(n, p)$ that satisfy the following condition, where $n$ is a positive integer and $p$ is a prime number. Condition) $2n-1$ is a divisor of $p-1$ and $p$ is a divisor of $4n^2+7$.
Source: 2024 KJMO P6
Tags: number theory, prime numbers
Find all pairs $(n, p)$ that satisfy the following condition, where $n$ is a positive integer and $p$ is a prime number. Condition) $2n-1$ is a divisor of $p-1$ and $p$ is a divisor of $4n^2+7$.