3 papers
math.NT2026
Complete classification of -adic Galois images for non-CM elliptic curves over $\Q$
Tho Nguyen Xuan
We solve Conjecture 1.6 of Furio and Lombardo [On -adic Galois representations for elliptic curves over $\Q$, Proc.\ London Math.\ Soc.\ (3) \textbf{133} (2026), e70193.]. As a…
math.NT2026
A proof of Hare's unfair conjecture
Tho Nguyen Xuan, Duc Hiep Pham, Huong Pham Lan
In this paper, we prove Hare's -unfair conjecture in [Computational progress on the unfair 0--1 polynomial conjecture, Experiment. Math. (2025), https://doi.org/10.1080/10586458…
math.GM2026
Integers representable as a difference of two rational fourth powers
Ashleigh Ratcliffe, Tho Nguyen Xuan
In Section 6.6 of the book {\it Number Theory, Volume I: Tools and Diophantine Equations, Graduate Texts in Mathematics, Volume 239, Springer (2007)}, Cohen investigated the solubi…