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Putnam 1958 November A5

Source: Putnam 1958 November

July 19, 2022
Putnammatrixcombinatorics

Problem Statement

Show that the number of non-zero integers in the expansion of the nn-th order determinant having zeroes in the main diagonal and ones elsewhere is n!(1−11!+12!−13!+⋯+(−1)nn!).n ! \left(1- \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \cdots + \frac{(-1)^{n}}{n!} \right) .
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