Hashing

h(x) is a hash function performed on an identifier x.

Show that if quadratic searching is carried out in the sequence (h(x) + q^2), (h(x) + (q-1)^2), ..., (h(x) + 1), h(x), (h(x) - 1), ..., (h(x) - q^2) with q = (b-1)/2, then the address difference % b between successive buckets being examined is b-2, b-4, b-6, ..., 5, 3, 1, 1, 3, 5, ..., b-6, b-4, b-2