  The paper considers a boundary value problem for the high-order
Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the
uniqueness of the solution are found. When substantiating the existence, the
problem of "small denominators" arises. Sufficient conditions for the
separability of the "small denominator" from zero are found. An example of a
boundary value problem not solvable by the Fourier method is given, in the
cases rectangle with integer side measurements.
