  We show that localized N-body soliton states exist for a quantum integrable
derivative nonlinear Schrodinger model for several non-overlapping ranges
(called bands) of the coupling constant \eta. The number of such distinct bands
is given by Euler's \phi-function which appears in the context of number
theory. The ranges of \eta within each band can also be determined completely
using concepts from number theory such as Farey sequences and continued
fractions. We observe that N-body soliton states appearing within each band can
have both positive and negative momentum. Moreover, for all bands lying in the
region \eta > 0, soliton states with positive momentum have positive binding
energy (called bound states), while the states with negative momentum have
negative binding energy (anti-bound states).
