MathDB

Consider a board of

a \times b

, with

a

and

b

integers greater than or equal to

2

. Initially their squares are colored black and white like a chess board. The permitted operation consists of choosing two squares with a common side and recoloring them as follows: a white square becomes black; a black box turns green; a green box turns white. Determine for which values of

a

and

b

it is possible, by a succession of allowed operations, to make all the squares that were initially white end black and all the squares that were initially black end white.
Clarification: Initially there are no green squares, but they appear after the first operation.

Problem Statement