Year: 2026
Type: preprint
Abstract: The solution of the Diophantine equation ay^2=b(x^k-c^k) is studied in different cases of k. Methods are proposed for different cases of k, which are convenient for computer algorithm implementation. The original equation is reduced to lower-degree equations, which can improve the efficiency in searching possible integer solutions. A sufficient condition of the unsolvability of ay^2=b(x^2n-c^2n) is presented.
Source: arXiv (Cornell University)
Authors: Zhuang, Xiaodong, Mastorakis, Nikos E.
Institutions: Qingdao University, Technical University of Sofia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216549963