MathDB

B5

Part of 1992 Putnam

Problems(1)

Putnam 1992 B5

Source: Putnam 1992

7/18/2022
Let DnD_n denote the value of the (n−1)×(n−1)(n -1) \times (n - 1) determinant (311…1141…1115…1⋮⋮⋮⋱⋮111…n+1). \begin{pmatrix} 3 & 1 &1 & \ldots & 1\\ 1 & 4 &1 & \ldots & 1\\ 1 & 1 & 5 & \ldots & 1\\ \vdots & \vdots & \vdots & \ddots & \vdots\\ 1 & 1 & 1 & \ldots & n+1 \end{pmatrix}. Is the set {Dnn! ∣ n≥2}\left\{ \frac{D_n }{n!} \, | \, n \geq 2\right\} bounded?
Putnamdeterminantbounded