MathDB

Let

a,b

be positive even integers. A rectangle with side lengths

a

and

b

is split into

a \cdot b

unit squares. Anja and Bernd take turns and in each turn they color a square that is made of those unit squares. The person that can't color anymore, loses. Anja starts. Find all pairs

(a,b)

, such that she can win for sure.
Extension: Solve the problem for positive integers

a,b

that don't necessarily have to be even. Note: The extension actually was proposed at first. But since this is a homework competition that goes over three months and some cases were weird, the problem was changed to even integers.

Problem Statement