MathDB
Problems
Contests
Undergraduate contests
Putnam
1969 Putnam
A2
A2
Part of
1969 Putnam
Problems
(1)
Putnam 1969 A2
Source: Putnam 1969
3/31/2022
Let
D
n
D_n
D
n
be the determinant of order
n
n
n
of which the element in the
i
i
i
-th row and the
j
j
j
-th column is
∣
i
−
j
∣
.
|i-j|.
∣
i
−
j
∣.
Show that
D
n
D_n
D
n
is equal to
(
−
1
)
n
−
1
(
n
−
1
)
2
n
−
2
.
(-1)^{n-1}(n-1)2^{n-2}.
(
−
1
)
n
−
1
(
n
−
1
)
2
n
−
2
.
Putnam
determinant