论文标题
在$λ_1U_{n_1} +λ_2U__{n_2} + \ ldots +λ_ku_{n_k} = wp_1^{z_1 {z_1} p_2^{z_2} {z_2} {z_2} \ cdots p_ss^{z_s^{
On the Diophantine equations of the form $λ_1U_{n_1} + λ_2U_{n_2} +\ldots + λ_kU_{n_k} = wp_1^{z_1}p_2^{z_2} \cdots p_s^{z_s}$
论文作者
论文摘要
在本文中，我们考虑二芬太汀方程$λ_1U_{n_1}+\ ldots+λ_ku_{n_k} = wp_1^{z_1} \ cdots p_s p_s^{z_s}大于或等于2的顺序序列； $ W $是固定的非零整数； $ p_1，\ dots，p_s $是固定的，不同的质数； $λ_1，\ dots，λ_k$是严格的正整数；和$ n_1，\ dots，n_k，z_1，\ dots，z_s $是非负整数未知数。我们证明了在解决方案$（n_1，\ dots，n_k，z_1，\ dots，z_s）$上的有效计算上限的存在。 在我们的证明中，我们在对数中使用线性形式的下限，扩展了Pink and Ziegler（2016），Mazumdar and Rout（2019），Meher和Rout（2017）和Ziegler（2019）的作品。
In this paper, we consider the Diophantine equation $λ_1U_{n_1}+\ldots+λ_kU_{n_k}=wp_1^{z_1} \cdots p_s^{z_s},$ where $\{U_n\}_{n\geq 0}$ is a fixed non-degenerate linear recurrence sequence of order greater than or equal to 2; $w$ is a fixed non-zero integer; $p_1,\dots,p_s$ are fixed, distinct prime numbers; $λ_1,\dots,λ_k$ are strictly positive integers; and $n_1,\dots,n_k,z_1,\dots,z_s$ are non-negative integer unknowns. We prove the existence of an effectively computable upper-bound on the solutions $(n_1,\dots,n_k,z_1,\dots,z_s)$. In our proof, we use lower bounds for linear forms in logarithms, extending the work of Pink and Ziegler (2016), Mazumdar and Rout (2019), Meher and Rout (2017), and Ziegler (2019).
