Eric Li

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math.NT2026

A Resolution of Erdős Problem 731 under Dyadic Regularity

Eric Li

We resolve Erdős 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 in…

math.NT2026

A Resolution of Erdős Problem 768: the Sylow Divisor Condition

Eric Li

We resolve Erdős Problem 768. Let $A (x)$ count the positive integers $n \leq x$ such that, for every prime $p ∣ n$ , there is a divisor $d > 1$ of $n$ with $d \equiv 1 (mod p)$ . Erdős…

math.NT2026

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

Eric Li

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

math.NT2026

Prime-Power Rarefaction and a Density-One Lower Bound for Erdős 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

Square-Annular Dynamics and Coalescence Frontiers for $n + τ (n)$

Eric Li

Let $T (n) = n + τ (n)$ , where $τ$ is the divisor function. We study the Erdos-Graham coalescence problem by encoding finite-level obstructions in the divisor-successor graph and in squa…

math.NT2026

Erdős Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations

Eric Li

For $0 \leq k \leq n$ , let $u (n, k)$ be the largest divisor of $(k n)$ whose prime factors are at most $k$ . Erdős Problem #684 concerns the special threshold $u (n, k) > n^{2}$ and asks…

A Resolution of Erdős Problem 731 under Dyadic Regularity

A Resolution of Erdős Problem 768: the Sylow Divisor Condition

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

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

Square-Annular Dynamics and Coalescence Frontiers for n+τ(n)

Erdős Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations

Square-Annular Dynamics and Coalescence Frontiers for $n + τ (n)$