{
  "id": "eulers-sum-of-powers-conjecture",
  "domain": "named-results",
  "type": "Disproven Conjecture",
  "title": "Euler's Sum of Powers Conjecture",
  "slug": "eulers-sum-of-powers-conjecture",
  "url": "/mathematics/named-results/eulers-sum-of-powers-conjecture/",
  "summary": "Conjectured 1769: at least n nth powers needed to sum to an nth power. Disproven for k=5 by Lander-Parkin 1966 (27⁵+84⁵+110⁵+133⁵=144⁵) and k=4 by Elkies 1988. One of the shortest published counterexample papers in mathematics.",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Lander, L.J. and Parkin, T.R. (1966). Bull. AMS, 72(6), 1079."
    },
    {
      "tier": 1,
      "citation": "Elkies, N.D. (1988). On A⁴+B⁴+C⁴=D⁴. Mathematics of Computation, 51(184), 825-835."
    },
    {
      "tier": 2,
      "citation": "Euler, L. (1769). Letter to Goldbach, 17 April 1769."
    },
    {
      "tier": 3,
      "citation": "Guy, R.K. (2004). Unsolved Problems in Number Theory. 3rd ed. Section D1."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5",
  "status": "disproven"
}