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Fermat–Catalan conjecture

generalization of Fermat's Last Theorem and Catalan's conjecture: a^m+b^n=c^k has only finitely many positive-integer solutions where a, b, c are coprime and m, n, k satisfy 1/m+1/n+1/k<1
Place conjecture Q851604
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Summary

Fermat–Catalan conjecture is a conjecture[1]. It draws 520 Wikipedia views per month (conjecture category, ranking #29 of 128).[2]

Key Facts

  • Named after: Pierre de Fermat[3]
  • Maintained by WikiProject: WikiProject Mathematics[4]

Why It Matters

Fermat–Catalan conjecture has Wikipedia articles in 14 language editions, a strong signal of global cultural recognition.[5] It is known by 17 alternative names across languages and contexts.[6]

Related Entities

Eugène Charles Catalan Pierre de Fermat

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [5] ↑ . Wikidata sitelinks. wikidata.org.
  3. [6] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Fermat–Catalan conjecture. Retrieved October 20, 2026, from https://4ort.xyz/entity/fermat-catalan-conjecture
MLA “Fermat–Catalan conjecture.” 4ort.xyz Knowledge Graph, 4ort.xyz, 20 Oct. 2026, https://4ort.xyz/entity/fermat-catalan-conjecture.
BibTeX @misc{4ortxyz_fermat-catalan-conjecture_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Fermat–Catalan conjecture}}, year = {2026}, url = {https://4ort.xyz/entity/fermat-catalan-conjecture}, note = {Accessed: 2026-10-20}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Fermat–Catalan conjecture — https://4ort.xyz/entity/fermat-catalan-conjecture (retrieved 2026-10-20)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 1d ago · Charp238 · 2026-10-19 view diff on Wikidata ↗
    Named after → Pierre de Fermat
    Defining formula → \left\{(a,b,c,m,n,k)\in(\mathbb Z^+)^6|1/m+1/n+1/k<1=\gcd\{a
    Instance of → conjecture
    Instance of → —
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ Defining formula: \left\{(a,b,c,m,n,k)\in(\mathbb Z^+)^6|1/m+1/n+1/k<1=\gcd\{a,b,c\}\right\}<\infty"
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