2 papers
math.NT2026
The density of long runs of non--free integers
Xinyang Jiang
Fix and let be the natural density of the such that none of is -free. We prove that $\log(1/D_k)=\frac{r-1}{ζ(r)}k\log k+\frac{r}{ζ(r)}k\log\lo…
math.GM2026
Counting Type I and Type II solutions of the Erdos-Straus equation: concentration, local obstructions, and a pointwise comparison
Xinyang Jiang
For a prime p >= 5 let f_I(p) and f_II(p) count the Type I and Type II solutions of the Erdos-Straus equation 4/p = 1/x + 1/y + 1/z, in the sense of Elsholtz and Tao. We do not add…