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Fermat's theorem on sums of two squares

theorem that an odd prime is a sum of two squares iff it is of the form 4𝑛+1
Intangible theorem Q914517
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Fermat's theorem on sums of two squares

Summary

Fermat's theorem on sums of two squares is a theorem[1]. It ranks in the top 10% of theorem entities by monthly Wikipedia readership (162 views/month).[2]

Key Facts

  • Fermat's theorem on sums of two squares's instance of is recorded as theorem[3].
  • Pierre de Fermat is named after Fermat's theorem on sums of two squares[4].
  • Fermat's theorem on sums of two squares's part of is recorded as list of theorems[5].
  • Fermat's theorem on sums of two squares's publication date is recorded as +1625-00-00T00:00:00Z[6].
  • Fermat's theorem on sums of two squares's Freebase ID is recorded as /m/060xk9[7].
  • Fermat's theorem on sums of two squares's defining formula is recorded as \forall p\in\mathbb P\colon\left((\exists m,n\in\mathbb Z\colon m^2+n^2=p)\iff p\not\equiv3\pmod4\right)[8].
  • Fermat's theorem on sums of two squares's MathWorld ID is recorded as Fermats4nPlus1Theorem[9].
  • Fermat's theorem on sums of two squares's maintained by WikiProject is recorded as WikiProject Mathematics[10].
  • Fermat's theorem on sums of two squares's copyright status is recorded as public domain[11].
  • Fermat's theorem on sums of two squares's copyright status is recorded as public domain[12].
  • Fermat's theorem on sums of two squares's Microsoft Academic ID is recorded as 66475981[13].
  • Fermat's theorem on sums of two squares's Brilliant Wiki ID is recorded as fermats-sum-of-two-squares-theorem[14].
  • Fermat's theorem on sums of two squares's PlanetMath ID is recorded as TheoremOnSumsOfTwoSquaresByFermat[15].
  • Fermat's theorem on sums of two squares's OpenAlex ID is recorded as C66475981[16].
  • Fermat's theorem on sums of two squares's Metamath statement ID is recorded as 2sq[17].

Why It Matters

Fermat's theorem on sums of two squares ranks in the top 10% of theorem entities by monthly Wikipedia readership (162 views/month).[2] It has Wikipedia articles in 18 language editions, a strong signal of global cultural recognition.[18] It is known by 21 alternative names across languages and contexts.[19]

Related Entities

Pierre de Fermat public domain

References

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

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . Freebase Data Dumps. wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . wikidata.org.
  14. [16] ↑ . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  15. [17] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [18] ↑ . Wikidata sitelinks. wikidata.org.
  3. [19] ↑ . 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's theorem on sums of two squares. Retrieved May 3, 2026, from https://4ort.xyz/entity/fermat-s-theorem-on-sums-of-two-squares
MLA “Fermat's theorem on sums of two squares.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/fermat-s-theorem-on-sums-of-two-squares.
BibTeX @misc{4ortxyz_fermat-s-theorem-on-sums-of-two-squares_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Fermat's theorem on sums of two squares}}, year = {2026}, url = {https://4ort.xyz/entity/fermat-s-theorem-on-sums-of-two-squares}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Fermat's theorem on sums of two squares — https://4ort.xyz/entity/fermat-s-theorem-on-sums-of-two-squares (retrieved 2026-05-03)

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