Erdős problem 1148 · problems.science

Can every large integer $n$ be written as $n=x^2+y^2-z^2$ with $\max(x^2,y^2,z^2)\leq n$ ?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

FormalConjectures/ErdosProblems/1148.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1148.leanErdos1148.erdos_11481 lineExact file

1True ↔ ∀ᶠ (n : ℕ) in Filter.atTop, Erdos1148.Erdos1148Prop n

SolvedStatement only, no proof

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

AI collaborating with humans
Erdős AI contributions wiki · 19 May, 2026
Machine
GPT-5.5 Pro
People
Ingo Althöfer, Przemek Chojecki
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AI collaborating with humans
Erdős AI contributions wiki · 24 Jan-16 Mar, 2026
Machine
Gemini 3 Pro, Gemini 3.1 Pro, GPT-5.2 Pro, GPT-5.2 Thinking, GPT-5.4 Pro
People
Ingo Althöfer, Przemek Chojecki, Wouter van Doorn
Open the source record
Formalization
Erdős AI contributions wiki · 17 Mar, 2026
Machine
Claude Opus 4.6, Gemini 3.1, GPT-5.4, UlamAI Prover
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argument
VibeMathed
Machine
Gemini 3 Pro, Gemini 3.1 Pro, GPT-5.2 Pro, GPT-5.2 Thinking, GPT-5.4 Pro, GPT-5.5 Pro
People
Ingo Althöfer, Przemek Chojecki, Wouter van Doorn
Reported outcome
resolved
Open the source record