On a variant of Pillai's problem with transcendental numbers

On a variant of Pillai's problem

In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a Tribonacci number.

On a variant of Pillai's problem II

In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences.

Pillai问题的一个函数域变体

A function field variant of Pillai's problem

本文研究复数域上一元函数域上Pillai问题的变体，证明在弱条件下简单线性递推序列方程仅有有限且可有效界定的解，且仅有有限个可有效计算的$f$具有多重表示。

关于涉及二次无理数收敛分母的皮莱问题变体

On a Variant of Pillai's problem involving convergent denominators of quadratic irrationals

针对二次无理数收敛分母序列，证明方程$q_{α,n}-q_{β,m}=c$有至少两个不同解时$c$仅有限个，且在特定实例中完全求解并列出所有解。

Mills常数变种的超越性

Transcendency of variants of Mills' constant

本文在黎曼ζ函数的密度假设下证明Mills常数是超越数，并给出了四类序列验证其算术性质的实例。

Combinatorial Applications of the Subspace Theorem

The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and the construction of transcendental numbers. But its usefulness extends beyond the realms of number theory. Other applications of the Subspace Theorem include linear recurrence sequences and finite automata. In fact, these structures are closely related to each other and the construction of transcendental numbers. The Subspace Theorem also has a number of rema…