  We describe a relation between the requirement of complete population
transfer in a four-mode system and the generating function of Pythagorean
triples from number theory. We show that complete population transfer will
occur if ratios between coupling coefficients exactly match one of the
Pythagorean triples (a; b; c) in Z, c^{2} = a^{2} + b^{2}. For a four-level
ladder system this relation takes a simple form (V12; V23; V34) ~ (c; b; a),
where coefficients Vij describe the coupling between modes. We find that the
structure of the evolution operator and the period of complete population
transfer are determined by two distinct frequencies. A combination of these
frequencies provides a generalization of the two-mode Rabi frequency for a
four-mode system.
