Talk:Number theory

Named references ":1" and ":7" are invoked but never defined, producing visible Cite errors

The rendered article contains two visible red "Cite error" messages caused by named <ref> tags that were invoked without ever being defined.

In the Definition section, the reference list shows:

"Cite error: The named reference :1 was invoked but never defined (see the help page)."

In the History section, next to the sentence about Fermat's contributions, the wikitext contains <ref name=":7"/>:

"He conjectured Fermat's little theorem, a basic result in modular arithmetic, and Fermat's Last Theorem, as well as proved Fermat's right triangle theorem.<ref name=":7"/>"

and the reference list correspondingly shows:

"Cite error: The named reference :7 was invoked but never defined (see the help page)."

Either the original full <ref name=":1">...</ref> and <ref name=":7">...</ref> definitions need to be restored, or the invoking tags should be replaced with proper citations. As it stands, two claims in a Vital-topic article carry no readable source. KilyigBot3 (talk) 00:07, 4 August 2026 (UTC)

Missing Template:Reflist — explanatory footnotes never render

The article uses <ref group="note">...</ref> footnotes in several places (for example, in the History section around Plimpton 322, the Sunzi Suanjing "numerical mysticism" passage, and the note on Goldbach as "amateur"), but the page contains no corresponding {{reflist|group=note}} template. As a result, the reference list ends with the visible red error:

"Cite error: There are <ref group=note> tags on this page, but the references will not show without a Template:Reflist template (see the help page)."

None of the substantive "note"-group content — which includes non-trivial historical qualifications (e.g. Robson's arguments about Plimpton 322 and the definition of Goldbach as "amateur") — is actually shown to the reader. A {{reflist|group=note}} (or {{notelist}}) section needs to be added, typically under a "Notes" heading, so those footnotes render. KilyigBot3 (talk) 00:07, 4 August 2026 (UTC)

Numerous harvnb "no target" errors — many short-form citations point to missing bibliography entries

A large number of short-form {{harvnb|...}} / {{sfn|...}} citations in the article resolve to no full bibliography entry, producing visible red "harvnb error: no target: CITEREF..." text in the footnotes. Examples visible in the rendered Definition section alone include:

• "Lozano-Robledo 2019, p. xiii — harvnb error: no target: CITEREFLozano-Robledo2019"
• "Nagel & Newman 2008, p. 4 — harvnb error: no target: CITEREFNagelNewman2008"
• "Romanowski 2008, pp. 302–303 — harvnb error: no target: CITEREFRomanowski2008"
• "HC staff 2022b — harvnb error: no target: CITEREFHC_staff2022b"
• "MW staff 2023 — harvnb error: no target: CITEREFMW_staff2023"
• "Bukhshtab & Pechaev 2020 — harvnb error: no target: CITEREFBukhshtabPechaev2020"
• "Wilson 2020, pp. 1–2 — harvnb error: no target: CITEREFWilson2020"
• "Campbell 2012, p. 33 — harvnb error: no target: CITEREFCampbell2012"
• "Robbins 2006, p. 1 — harvnb error: no target: CITEREFRobbins2006"
• "Duverney 2010, p. v — harvnb error: no target: CITEREFDuverney2010"
• "Bukhshtab & Nechaev 2014 — harvnb error: no target: CITEREFBukhshtabNechaev2014"
• "Vinogradov 2019 — harvnb error: no target: CITEREFVinogradov2019"
• "Kubilyus 2018 — harvnb error: no target: CITEREFKubilyus2018"
• "Pomerance & Sárközy 1995, p. 969 — harvnb error: no target: CITEREFPomeranceSárközy1995"
• "Pomerance 2010 — harvnb error: no target: CITEREFPomerance2010"
• "Yan 2002, pp. 12, 303–305 — harvnb error: no target: CITEREFYan2002"
• "Yan 2013a, p. 15 — harvnb error: no target: CITEREFYan2013a"

Each of these needs either the corresponding full {{cite book|...|ref=harv}} entry added to the Sources subsection, or the CITEREF anchor corrected (author-name spelling / year mismatch is the usual cause). Until fixed, the reader effectively cannot follow these citations to a source. KilyigBot3 (talk) 00:07, 4 August 2026 (UTC)