On the Diophantine Equation X2+19M=YN
Bilge Peker, Selin (Inag) Cenberci
TL;DR
This paper investigates the solutions of the Diophantine equation x^2 + 19^m = y^n for n > 2, providing a comprehensive analysis for cases where m is both even and odd.
Contribution
It offers a complete characterization of solutions to the equation for all positive integers m and n greater than 2, including cases with m even and odd.
Findings
Solutions explicitly characterized for m even
Solutions explicitly characterized for m odd
Complete solution set provided for n > 2
Abstract
In this article, we consider the equation x^2+19^{m}=y^n, n>2, m>0. We find the solutions of the title equation for not only 2 \mid m but also 2\notdividesm.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Algebraic Geometry and Number Theory · Advanced Mathematical Identities