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Extended Euclidean algorithm

Method for computing the relation of two integers with their greatest common divisor

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionJul 27, 2026
Entity authoritySource title only
Source-derived summary

In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that ; it is generally denoted as .

Editorial summary

This brief starts where responsible research should: with the source description of “Extended Euclidean algorithm” as method for computing the relation of two integers with their greatest common divisor. Everything that follows is an evidence route, not borrowed authority.

Editorial reviewUseful for establishing the present vocabulary of the subject while preserving a route back to the evidence on which that vocabulary rests. The current 52-word lead offers orientation but no explicit four-digit date, so chronology should not be assumed. The selected authority fields contribute no independent date. The account is most persuasive where Extended, Euclidean and algorithm can be independently traced.
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Why this record matters

The subject matters to the science & nature register because the source frames it as method for computing the relation of two integers with their greatest common divisor. Its deeper value depends on whether names, dates, institutions and citations support that framing.

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The date and method of observation matter as much as the stated conclusion, especially where classification or consensus has changed. The source revision retrieved here is dated Jul 27, 2026.

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This entry incorporates text from “Extended Euclidean algorithm” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.