Question

The sequence of integers X₁ with n≥1 is defined by x₁ = 1, X₂ = A, and Xn=(2n + 1) x_{n-1}-\left(n^{2}-1\right) x_{n-2} \text { for } n \geq 3 \text {, } where A is a positive integer. For which values of A do we have x₁ which divides x; for all i≤j ?

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