Let {Pn}n≥0 be the sequence of Padovan numbers defined by P0=0, P1=P2=1, and Pn+3=Pn+1+Pn for all n≥0. In this paper, we find all positive square-free integers d≥2 such that the Pell equations x2−dy2=ℓ, where ℓ∈{±1,±4}, have at least two positive integer solutions (x,y) and (x′,y′) such that each of x and x′ is a product of two Padovan numbers