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We consider the Brocard-Ramanujan type Diophantine equation P(z) = n! + m!, where P is a polynomial with rational coefficients. We show that the ABC Conjecture implies that this equation has only finitely many integer solutions when d ≥ 2 and $P\left(z\right)=a_d{z}^d+a_{d-3}{z}^{d-3}+\cdots +a₁x+a₀$.