MathDB

The infinite integer plane

Z\times Z = Z^2

consists of all number pairs

(x, y)

, where

x

and

y

are integers. Let

a

and

b

be non-negative integers. We call any move from a point

(x, y)

to any of the points

(x\pm a, y \pm b)

(x \pm b, y \pm a)

(a, b)

-knight move. Determine all numbers

a

and

b

, for which it is possible to reach all points of the integer plane from an arbitrary starting point using only

(a, b)

-knight moves.

3