ALT (画像の式を表すLaTeXコマンド。※直打ちメモ。文字数制限のため途中まで) F_{n_1}F_{n_2}\cdots F_{n_k}=m_1!\cdots m_t! \\ (3 \leqq n_1 < n_2 <\cdots < n_k, \quad 2 \leqq m_1 \leqq m_2 \leqq \cdots \leqq m_t) \\ の条件下で、フィボナッチ数の積が階乗数の積になるのは有限個。次の \ 30 \ 通りに限られる。 \\ \text{(Florian Luca, Pantelimon Stănică　2005)} 　\\ \begin{aligned} F_3 &= {\color{red}{2!}}\\ F_3F_4 &= {\color{red}{3!}}\\ F_6 &= (2!)^3\\ F_3F_6 &= (2!)^4\\ F_4F_6 &= {\color{red}{4!}}\\ F_3F_4F_6 &= 2!4!\\ F_4F_5F_6 &= {\color{red}{5!}}\\ F_{12} &= 3!4!\\ F_3F_4F_5F_6 &= 2!5!\\ F_3F_{12} &= 2!3!4!\\ F_4F_{12} &= 2!(3!)^3\\ F_5F_{12} &= 3!5!\\ F_3F_4F_{12} &= (3!)^2 4!\\ F_6F_{12} &= 2!(4!)^2\\ F_3F_5F_{12} &= 2!3!5!\\ F_3F_6F_{12} &= (2!)^2(4!)^2\\ F_4F_6F_{12} &= 3!(4!)^2\\ F_3F_4F_5F_{12} &= (3!)^2 5!\\ F_3F_4F_5F_6F_8 &= {\color{red}{7!}}\\ F_5F_6F_{12} &= 2!4!5!\\ F_3F_4F_6F_{12} &= 2!3!(4!)^2\\ F_3F_5F_6F_{12} &= (2!)^2 4!5!\\ F_4F_5F_6F_{12} &= 3!4!5!\\ F_3F_5F_8F_{12} &= 3!7!\\ F_3F_4F_5F_6F_{12} &= 2!3!4!5!\\ ※以下省略 \end{aligned}