Abstract
A simple one-dimensional model is proposed, in which N spinless interacting fermions occupy M>N degenerate states on a circle. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors $\nu N/M=1/(2m+1)$. Within this model the complimentary wavefunction for $\nu =l-I/(2m+1)$ is found explicitly.