Problem #72
Let M_{n} denote the n×n
matrix whose first row consists of
the integers 1,2,3,...,n in order and each row is a cyclic shift
(to the right) of the previous row. For example M_{4} is
shown below.
1

2

3

4

4

1

2

3

3

4

1

2

2

3

4

1

Find det(M_{n}).