MathDB

Let

E

be the set of

1983^3

points of the space

\mathbb R^3

all three of whose coordinates are integers between

0

and

1982

(including

0

and

1982

). A coloring of

E

is a map from

E

to the set {red, blue}. How many colorings of

E

are there satisfying the following property: The number of red vertices among the

8

vertices of any right-angled parallelepiped is a multiple of

4

13