Given a prime number $p$, find the number of pairs of integers $(a, b)$ such that $p \lt a$, $p \lt b$ and $ab$ is divisible by $(a-p)(b-p)$.
Number of integral solutions
2
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elementary-number-theory
prime-numbers
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0From divisors of $p^2+p$ one gets the simplest solutions. – 2011-12-03