The Hidden Prime

Algebra Level 3

\[\dfrac{x^2 - P}{(x - 2)(x - 3)(x - 5)} = \dfrac{A}{x - 2} + \dfrac{B}{x - 3} + \dfrac{C}{x - 5}\]

The equation above represents a partial fraction decomposition for constants \(A,B,C\) and \(P\).

What is the smallest value of the prime number \(P \) such that \(A,B\) and \(C\) are all integers?

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