✦ 5 frontiers

read-only vieweressays

erdős #1148

← #1147 · #1149 → (packet.json; erdosproblems.com)

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

Worked, still open.

number theory · solved · formalized (Lean) · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 11 · solved (literature)

theorem erdos_1148 : answer(True) ↔ ∀ᶠ n in atTop, Erdos1148Prop n

formal-conjectures/1148.lean ↗

oeis

A390380 — Integers k which cannot be written in the form x^2 + y^2 - z^2, where x, y, z are integers and x^2, y^2, z^2 <= k.3,6,11,15,22,27,35,38,42,55,59,66,78,83,87,95,110,118,123,131,143,150,187,210,222,227,255,262,266,278,299,303,323,326,39 A393168 — Integers k which can be written in the form x^2 + y^2 - z^2, where x, y, z are integers and x^2, y^2, z^2 <= k.0,1,2,4,5,7,8,9,10,12,13,14,16,17,18,19,20,21,23,24,25,26,28,29,30,31,32,33,34,36,37,39,40,41,43,44,45,46,47,48,49,50,51

links

Chojecki and GPT-5.4 Pro · paper

status

solved

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub