A proof of Hare's $ε$ unfair conjecture
In this paper, we prove Hare's $ε$-unfair conjecture in [Computational progress on the unfair 0--1 polynomial conjecture, Experiment. Math. (2025), https://doi.org/10.1080/10586458.2025.2527786].
math.NT↗
arXiv subjects
Tho Nguyen Xuan
Publications and source records attributed to Tho Nguyen Xuan.
Integers representable as a difference of two rational fourth powers
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 solubility of the equation $n=x^4+y^4$ in the rational numbers $x,y$ for all positive integers $n \leq 10000$. Motivated by this, we investigate the equation $n=x^4-y^4$ and obtain the complete list of positive integers $n\leq 10000$ that can be represented in this form for some nonzero rational numbers $x$ and $y$.
math.GM↗