A homogeneous linear conjugation problem on a closed contour is considered for a three-dimensional piecewise analytic vector. To each of its solutions there corresponds a triple of functions that are the ratios of the boundary values on the contour of the respective components of this solution. Relations are given that connect the elements of the H-continuous matrix function of the problem and ensure the existence of two of its solutions for which the corresponding components of the associated triples differ by rational factors, while the problem itself admits a closed-form solution.
S. N. Kiyasov (Sat,) studied this question.