Eric Li

works on

analytic number theory 1 asymptotic analysis 1 divisor conditions 1 erdos problems 1 formal verification 1 proof assistants 1

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math.NT2026

A Resolution of ErdÅs Problem 768: the Sylow Divisor Condition

Eric Li

The paper solves Erdős Problem 768 by determining the exact leading constant in the asymptotic formula for the proportion of integers whose every prime divisor has a co‑divisor con…

math.NT2026

A Resolution of ErdÅs Problem 731 under Dyadic Regularity

Eric Li

We resolve ErdÅs Problem 731 under the explicit dyadic-regularity formalization of "reasonable." Let $A (n)$ be the least positive integer not dividing $(n 2 n)$ . On dyadic i…

math.NT2026

A resolution of ErdÅs Problem 1061 on the sum-of-divisors function

Eric Li

We resolve ErdÅs Problem 1061, the question whether the number \[ S(x)=\#\{(a,b)\in\mathbb{N}^2:a+b\le x, \ Ï(a)+Ï(b)=Ï(a+b)\} \] of ordered solutions has a linear asymptotic $…

math.NT2026

Prime-Power Rarefaction and a Density-One Lower Bound for ErdÅs Problem 400

Eric Li

For fixed $k \geq 2$ , let $g_{k} (n)$ be the greatest excess $a_{1} + \dots + a_{k} - n$ among positive integers $a_{i}$ satisfying $a_{1}! \dots a_{k}! ∣ n!$ . We prove that, for every $\varepsilon>…

math.NT2026

Rank Amplification for Shifted Equal Values of Euler's Totient Function

Eric Li

Let $S_{h}^{φ} (x)$ denote the number of integers $n \leq x$ for which $φ (n) = φ (n + h)$ . For the unit shift, we prove $S_{1}^{φ} (x) ≪ x exp - (1/2 - o (1)) lo g x, lo g_{2} x$ . More generally,…

math.NT2026

An Average-Order Theorem for a Shifted Pairwise-Coprime Extremal Problem

Eric Li

For $n \geq 2$ , let $M (n)$ be the supremum of $\sum_{a \in A} 1/ (n - a)$ over pairwise coprime sets $A \subset [1, n)$ . Erdős asked whether $M (n) \leq \sum_{p < n} 1/ p + O (1)$ uniformly in $n$ . We…

A Resolution of ErdÅs Problem 768: the Sylow Divisor Condition

A Resolution of ErdÅs Problem 731 under Dyadic Regularity

A resolution of ErdÅs Problem 1061 on the sum-of-divisors function

Prime-Power Rarefaction and a Density-One Lower Bound for ErdÅs Problem 400

Rank Amplification for Shifted Equal Values of Euler's Totient Function

An Average-Order Theorem for a Shifted Pairwise-Coprime Extremal Problem

A Resolution of ErdÅs Problem 768: the Sylow Divisor Condition

A Resolution of ErdÅs Problem 731 under Dyadic Regularity

A resolution of ErdÅs Problem 1061 on the sum-of-divisors function

Prime-Power Rarefaction and a Density-One Lower Bound for ErdÅs Problem 400