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Putnam 1969 A2

Source: Putnam 1969

March 31, 2022
Putnamdeterminant

Problem Statement

Let DnD_n be the determinant of order nn of which the element in the ii-th row and the jj-th column is ∣i−j∣.|i-j|. Show that DnD_n is equal to (−1)n−1(n−1)2n−2.(-1)^{n-1}(n-1)2^{n-2}.
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