AI 中文总结
研究含雅各布斯塔尔数和斐波那契数的丢番图方程，核心方法是对数线性形式技术，主要贡献是确定\(2<k<l<m\)时，丢番图方程\(F_kF_lF_m = J_n\)唯一解为\((k,l,m,n)=(5,7,8,12)\)。
AI 中文摘要
在本文中，我们确定了所有可表示为三个斐波那契数乘积的雅各布斯塔尔数。具体而言，我们的主要结果表明，对于\(2<k<l<m\)，丢番图方程\(F_kF_lF_m = J_n\)的唯一解是\((k,l,m,n)=(5,7,8,12)\)。证明依赖于涉及对数线性形式的技术。
英文摘要
In the present paper, we identify all Jacobsthal numbers that may be expressed as a product of three Fibonacci numbers. More precisely, our main result shows that the only solution to the Diophantine equation \[ F_kF_lF_m=J_n \] for $2<k<l<m$ is \[ (k,l,m,n)=(5,7,8,12). \] The proof relies on techniques involving linear forms in logarithms.
Comments12 pages. Final version. To appear in Hacettepe Journal of Mathematics and Statistics
