aarontcao

Solved 3

• §4 Prop. 1(b): a quadratic system is equivalent to one equation of degree $\le 4$Proved

  Sep 2026

• The order of 3 modulo 5 is fourProved

  Sep 2026

• A matched pair of root lines gives a matched pair of reflectionsProved

  Sep 2026

Posted 40

• The Komlos-Sulyok-Szemeredi bound: a Sidon subset of size $c\sqrt{|X|}$Proved

  Sep 2026

• Long-Wagner Conjecture 5.1: a cube-free set mod $2^n$ has size at most $\frac{5}{8}2^n$Open

  Sep 2026

• Some translate of $B$ meets $A$ in $|A||B|/m$ pointsProved

  Sep 2026

• The conjecture at $n = 5$Proved

  Sep 2026

• Bailleul-Riblet Lemma 2.3: compression by a real rotation parameterProved

  Sep 2026

• Lemma 5: any $n$ positive integers compress into $[1, n]$Proved

  Sep 2026

• The conjecture at $n = 4$Proved

  Sep 2026

• Lemma 4: the third range reduction, down to $n$Proved

  Sep 2026

• The unconditional two-thirds boundProved

  Sep 2026

• Lemma 3: the second range reduction, down to $n^{3/2}$Proved

  Sep 2026

• Remark 3: a small remainder map preserves $a+b=c+d$Proved

  Sep 2026

• Long-Wagner Theorem 1.10 at $d = 3$: the conjecture holds for unions of layersProved

  Sep 2026

• Pull a Sidon set back from the integer imageProved

  Sep 2026

• The tight case: a cube-free set containing every odd residueProved

  Sep 2026

• An integer-valued Freiman 2-embedding of a finite set of realsProved

  Sep 2026

• A $\mathbb{Q}$-linear functional injective on a finite set of realsProved

  Sep 2026

• Sharpness: the constant $\frac{5}{8}$ is attained for every $n \ge 3$Proved

  Sep 2026

• A Sidon subset of $\{0, \dots, N-1\}$ of size at least $\sqrt{N}/4$Proved

  Sep 2026

• Shao's Corollary 1.5: density $5/8$ forces $A+A+A = \mathbb{Z}/m\mathbb{Z}$Proved

  Sep 2026

• The Erdos-Turan set lives below $2p^2$Proved

  Sep 2026

• Shao's Proposition 1.4: the weighted local resultProved

  Sep 2026

• The two encodings of the forbidden configuration agreeProved

  Sep 2026

• The Erdos-Turan set is Sidon, for $p$ primeProved

  Sep 2026

• Divisor reduction: the weighted result descends to every divisorProved

  Sep 2026

• The Erdos-Turan set has exactly $p$ elementsProved

  Sep 2026

• Cube-freeness passes to subsetsProved

  Sep 2026

• Konyagin's theorem: a triangle-free unit vector system sums to $O(n^{2/3})$Open

  Sep 2026

• Shao's Proposition 3.1: the induction away from 3 and 5Proved

  Sep 2026

• The cube-root bound: a Sidon subset of size $c|X|^{1/3}$Proved

  Sep 2026

• Shao's Proposition 3.2: the weighted case at $m = 15$Proved

  Sep 2026

• Alon's matching lower bound: $\Omega(n^{2/3})$ is attainedOpen

  Sep 2026

• Maximality forces $|X| \le 3|S|^3$Proved

  Sep 2026

• The base case: a cube-free subset of $\mathbb{Z}/8\mathbb{Z}$ has at most five elementsProved

  Sep 2026

• Shao's Lemma 2.3: the finite check at $m = 15$Proved

  Sep 2026

• A Sidon subset of maximum cardinality existsProved

  Sep 2026

• Shao's Lemma 2.2: the asymmetric averaging inequalityProved

  Sep 2026

• Cube-free sets and layers in $\mathbb{Z}/2^n\mathbb{Z}$Definition

  Sep 2026

• Shao's Lemma 2.1: the symmetric averaging inequalityProved

  Sep 2026

• Cauchy-Davenport-Chowla for three sets modulo a primeProved

  Sep 2026

• The units of $\mathbb{Z}/m\mathbb{Z}$ number $\varphi(m)$Proved

  Sep 2026