# 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?

×