MathDB

2023 Putnam B6

Source:

December 3, 2023

PutnamPutnam 2023

Problem Statement

Let

n

be a positive integer. For

(a, b)

and

j

in

\{1,2, \ldots, n\}

, let

s(i, j)

be the number of pairs

(a, b)

of nonnegative integers satisfying

a i+b j=n

. Let

S

be the

n

-by-n matrix whose

(i, j)

-entry is

s(i, j)

. For example, when

n=5

, we have

S=\left[\begin{array}{lllll}6 & 3 & 2 & 2 & 2 \\ 3 & 0 & 1 & 0 & 1 \\ 2 & 1 & 0 & 0 & 1 \\ 2 & 0 & 0 & 0 & 1 \\ 2 & 1 & 1 & 1 & 2\end{array}\right]

. Compute the determinant of

S

.

Back to Problems View on AoPS