Samuel Korsky

activity

20192026

most citedOn the Computational Power of RNNs

19 citations · 19 across the 19 of their papers we have counts for

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6 papers · 1 filter

math.NT2026

Affine Copies of Three-Point Patterns in Sets of Integers

Samuel Korsky

Let $P = {0, a, b}$ , where $0 < a < b$ and $g cd (a, b) = 1$ . For a finite set $A \subset Z$ , let $M_{P}^{+} (A)$ count the copies $x, x + a d, x + b d \in A$ with $d > 0$ , and let $M_{P} (A)$ count the…

math.NT2026

Improved Bounds for Distinct Multiples in Intervals

Kaizhe Chen, Samuel Korsky

For $n \geq 1$ , let $F (n)$ be the least $H$ such that any $H$ consecutive integers contain $n$ pairwise distinct integers $a_{1}, a_{2}, \dots, a_{n}$ with $k ∣ a_{k}$ for $1 \leq k \leq n$ , a…

math.NT2026

Positive Lower Density for Hofstadter's $ab - 1$ Problem

Samuel Korsky

Let $A$ be the smallest set of positive integers containing $2$ and $3$ such that $ab - 1 \in A$ whenever $a, b \in A$ are distinct. We prove that $A$ has positive lower density, answer…

math.NT2026

Large Sets of Integers with No Harmonic Triples

Samuel Korsky

Let $f (N)$ denote the largest size of a set $A \subseteq [N] = {1, \dots, N}$ containing no distinct $a, b, c$ such that \[ \frac2a=\frac1b+\frac1c . \] We prove \[ f(N)\gg N\exp\!\lef…

math.NT2026

A Stretched-Exponential Bound for an Erdos--Graham Unit-Fraction Problem

Samuel Korsky

For a finite multiset $A$ of positive integers, write $R (A) = \sum_{a \in A} a^{- 1}$ and let $ε (A)$ be the distance from $1$ to the largest reciprocal subsum of $A$ …

math.NT2026

Inhomogeneous Approximation by Sums of Roots

Samuel Korsky

Let $d \geq 2$ and $k \geq 1$ be fixed. We prove that, for every $ε > 0$ and every real $β$ , there exist integers $1 \leq b_{1}, \dots, b_{k} \leq N$ such that \[ \left\|\sum_{j=1}^k b_j^{1/d…

Affine Copies of Three-Point Patterns in Sets of Integers

Improved Bounds for Distinct Multiples in Intervals

Positive Lower Density for Hofstadter's ab−1 Problem

Large Sets of Integers with No Harmonic Triples

A Stretched-Exponential Bound for an Erdos--Graham Unit-Fraction Problem

Inhomogeneous Approximation by Sums of Roots

Positive Lower Density for Hofstadter's $ab - 1$ Problem