In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tori. We present two results. We first show that on the torus $(\mathbb{ R}/2\pi\mathbb{ Z})^{ 2}$, a non-constant eigenfunction has an even number of nodal domains. We then consider the torus $(\mathbb{ R}/2\pi\mathbb{ Z})\times(\mathbb{ R}/2\rho\pi\mathbb{ Z})\,$, with $\rho=\frac{ 1}{ \sqrt{ 3}}\,$, and construct on it an eigenfunction with three nodal domains.
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