  We study the map degrees between quasitoric 4-manifolds. Our results rely on
Theorems proved by Duan and Wang. We determine the set D (M, N) of all possible
map degrees from M to N when M and N are certain quasitoric 4-manifolds. The
obtained sets of integers are interesting, e. g. those representable as the sum
of two squares D (C P^2#C P^2, C P^2) or the sum of three squares D (C P^2 # C
P^2 # C P^2, C P^2). Beside the general results about the map degrees between
quasitoric 4-manifolds, the connections among Duan-Wang's approach, the
quadratic forms, the number theory and the lattices is established.
