arXiv subjects
Publications and source records attributed to Rui-Jing Wang.
In this paper, it is proved that there is an arithmetic progression of positive integers such that each of which is expressible neither as $p+F_m$ nor as $q+L_n$, where $ p,q $ are primes, $ F_m $ denotes the $ m $-th Fibonacci number and $ L_n $ denotes the $ n $-th Lucas number.
For any positive integer $n$, let $σ(n)$ be the sum of all positive divisors of $n.$ In this paper, it is proved that the set of positive integers $ n $ for which $ σ(30n+1)\geq σ(30n) $ has a density less than $ 0.0371813, $ which answers a recent problem of Pongsriiam in part.
For any positive integer $n$, let $σ(n)$ be the sum of all positive divisors of $n.$ In this paper, it is proved that for every integer $ 1\leq k\leq 29,\ (k,30)=1, $ we have $$\sum_{n\leq K}σ(30n)>\sum_{n\leq K}σ(30n+k)$$ for all $K\in \mathbb{N},$ which gives a positive answer to a problem posed by Pongsriiam recently.