Skolem 猜想在一类指数方程上的证实, II
数论
2021-05-04 v1
摘要
根据 Skolem 猜想,若一个指数丢番图方程不可解,则它在某个适当选取的模下也不可解。除若干具体方程外,该猜想仅在相当特殊的情形中被证明。本文中,我们证明了该猜想对形如 的方程成立,其中 为固定整数,而 为非负整数未知量。该结果推广了 Hajdu 与 Tijdeman 近期的一个定理。
引用
@article{arxiv.2105.00415,
title = {Skolem's conjecture confirmed for a family of exponential equations, II},
author = {A. Bérczes and L. Hajdu and R. Tijdeman},
journal= {arXiv preprint arXiv:2105.00415},
year = {2021}
}
备注
The paper appeared in Acta Arithmetica. Here we correct a typo: on page 134 in line 5, the modulus $m'$ should read as $m'=|y^{s_N}(x^{o_N}-1)|$. (Like here on page 6 in line 7 up.) We are very much grateful to Reese Scott and Robert Styer for pointing out this error