MathDB

One tiles a floor of

a \times b

^2

with square tiles,

a,b \in N

. Tiles do not overlap, and sides of floor and tiles are parallel. Using tiles of

2\times 2

^2

leaves the same amount of floor uncovered as using tiles of

4\times 4

^2

. Using

3\times 3

^2

tiles leaves

29

^2

floor uncovered. Determine

a

and

b

2