22 citations · 137 across the 47 of their papers we have counts for
5 papers · 1 filter
Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
Shaofang Hong, Scott D. Kominers
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any in…
Squares in (2^2-1)...(n^2-1) and p-adic valuation
Shaofang Hong, Xingjiang Liu
In this paper, we determine all the squares in the sequence . From this, one deduces that there are infinitely many squares in this sequence…
Infinite divisibility of Smith matrices
Shaofang Hong
Given an arithmetical function , by and we denote the function evaluated at the greatest common divisor of positive integers and and eva…
Asymptotic behavior of the smallest eigenvalue of matrices associated with completely even functions (mod r)
Shaofang Hong, Raphael Loewy
In this paper we present systematically analysis on the smallest eigenvalue of matrices associated with completely even functions (mod ). We obtain several theorems on the asymp…
The universal Kummer congruences
Shaofang Hong, Jianrong Zhao, Wei Zhao
Let be a prime. In this paper, we present a detailed -adic analysis to factorials and double factorials and their congruences. We give good bounds for the -adic sizes of…