TheoremDB

Problem packetResearch packetR1348

R1348Sourced evidence

Current status and unresolved remainder

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Authored summary

UNKNOWN as of 2026-08-01. Primitive-divisor theorems sharply constrain large indices in Lucas sequences, but the exact pair classification for this recurrence was not located in the checked sources.

The record cites sources for its explanation.

Recorded status: reported

Recorded scope: No scope is recorded.

Originating problem: Square-class collisions in the Pell-Lucas sequence

Authored record and scope
Authored title
Current status and unresolved remainder
Record type
claim
Stored status
reported
Evidence grade
sourced

2Authored explanation

UNKNOWN as of 2026-08-01. Primitive-divisor theorems sharply constrain large indices in Lucas sequences, but the exact pair classification for this recurrence was not located in the checked sources.

The search checked the exact statement, parameters, equivalent terminology, and the sources listed in this packet. Database silence is treated only as bounded status evidence. A complete resolution must satisfy every acceptance condition in the canonical problem.

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Replay material: source only

3Evidence

Replay package: source only

A verification source is cited. This record has no executable replay attached.

Verification source: doi.org ↗, Main primitive-divisor theorem and its exceptional small indices

4How it connects

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Recorded for

Machine-readable record

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  "ref": "R1348",
  "content_hash": null,
  "slug": "pell-lucas-squareclass-collisions-status-20260801",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-08-01. Primitive-divisor theorems sharply constrain large indices in Lucas sequences, but the exact pair classification for this recurrence was not located in the checked sources.",
  "relevance": "For pell lucas squareclass collisions, pins the dated research frontier: UNKNOWN as of 2026-08-01. Primitive-divisor theorems sharply constrain large indices in Lucas sequences, but the exact pair classification for this recurrence was not located in the checked sources.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-08-01. Primitive-divisor theorems sharply constrain large indices in Lucas sequences, but the exact pair classification for this recurrence was not located in the checked sources.\n\nThe search checked the exact statement, parameters, equivalent terminology, and the sources listed in this packet. Database silence is treated only as bounded status evidence. A complete resolution must satisfy every acceptance condition in the canonical problem.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1515/crll.2001.080",
      "locator": "Main primitive-divisor theorem and its exceptional small indices"
    },
    "missing": [
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      "command",
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      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1515/crll.2001.080",
    "locator": "Main primitive-divisor theorem and its exceptional small indices"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1347",
      "title": "Resolve the stated acceptance conditions",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "pell-lucas-squareclass-collisions",
      "title": "pell lucas squareclass collisions",
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}

6Provenance

View source, identifiers, and projection details

A statement this project treats as settled at the recorded evidence grade, with the work that backs it.

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