$\mathop \prod \limits_{i = 0}^n \left( {1 - {x^{\frac{1}{{{2^{i + 1}}}}}} + {x^{\frac{1}{{{2^i}}}}}} \right) = \mathop \sum \limits_{\matrix
{0 \leqslant i \leqslant {2^{{\text{n}} - 1}} - 1} \\
{i \equiv 0,1\left( {mod\;3} \right)} \\ } {\left( { - 1} \right)^i}\left( {{x^{\frac{i}{{{2^n}}}}} + {x^{\frac{{{2^n} - i}}{{{2^n}}}}}} \right)$ |