[math] \newcommand{\mathds}{\mathbb}[/math]

Prove that the only Hadamard matrix at [math]N=5[/math] is the Fourier matrix,

[[math]] F_5=\begin{pmatrix} 1&1&1&1&1\\ 1&w&w^2&w^3&w^4\\ 1&w^2&w^4&w&w^3\\ 1&w^3&w&w^4&w^2\\ 1&w^4&w^3&w^2&w \end{pmatrix} [[/math]]

with [math]w=e^{2\pi i/5}[/math], up to the standard equivalence relation for such matrices.