MathDB

The lateral sides of a box with base

a\times b

and height

c

(where

a

;

b

;

c

are natural numbers) are completely covered without overlap by rectangles whose edges are parallel to the edges of the box, each containing an even number of unit squares. (Rectangles may cross the lateral edges of the box.) Prove that if

c

is odd, then the number of possible coverings is even. D. Karpov, C. Gukshin, D. Fon-der-Flaas

Problem Statement