Reduced residue system

en

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Reduced residue system

Quality:

Reduced residue system - set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n. Article “Reduced residue system” in English Wikipedia has 20.1 points for quality (as of July 1, 2025). The article contains 4 references and 5 sections.

This article has the best quality in Polish Wikipedia. However, this article is the most popular in English version.

Since the creation of article “Reduced residue system”, its content was written by 16 registered users of English Wikipedia and edited by 29 registered Wikipedia users in all languages.

The article is cited 7 times in English Wikipedia and cited 26 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #147119 in February 2012
  • Global: #183589 in October 2014

The highest popularity rank from 2008:

  • Local (English): #573196 in March 2014
  • Global: #908573 in October 2020

There are 6 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1Polish (pl)
Zredukowany układ reszt modulo
22.8247
2English (en)
Reduced residue system
20.1466
3Galician (gl)
Sistema reducido de residuos
18.5882
4Arabic (ar)
نظام بواقي مصغر
17.1933
5Hungarian (hu)
Redukált maradékrendszer
5.5141
6Dutch (nl)
Reststelsel
5.1596
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Reduced residue system" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Reduced residue system
163 772
2Hungarian (hu)
Redukált maradékrendszer
13 897
3Polish (pl)
Zredukowany układ reszt modulo
1 599
4Arabic (ar)
نظام بواقي مصغر
1 253
5Dutch (nl)
Reststelsel
1 065
6Galician (gl)
Sistema reducido de residuos
77
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Reduced residue system" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Reduced residue system
423
2Hungarian (hu)
Redukált maradékrendszer
30
3Polish (pl)
Zredukowany układ reszt modulo
11
4Galician (gl)
Sistema reducido de residuos
10
5Arabic (ar)
نظام بواقي مصغر
3
6Dutch (nl)
Reststelsel
0
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Reduced residue system" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Reduced residue system
16
2Dutch (nl)
Reststelsel
4
3Arabic (ar)
نظام بواقي مصغر
3
4Hungarian (hu)
Redukált maradékrendszer
3
5Polish (pl)
Zredukowany układ reszt modulo
2
6Galician (gl)
Sistema reducido de residuos
1
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Reduced residue system" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Arabic (ar)
نظام بواقي مصغر
0
2English (en)
Reduced residue system
0
3Galician (gl)
Sistema reducido de residuos
0
4Hungarian (hu)
Redukált maradékrendszer
0
5Dutch (nl)
Reststelsel
0
6Polish (pl)
Zredukowany układ reszt modulo
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Reduced residue system" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1Hungarian (hu)
Redukált maradékrendszer
13
2English (en)
Reduced residue system
7
3Arabic (ar)
نظام بواقي مصغر
2
4Galician (gl)
Sistema reducido de residuos
2
5Dutch (nl)
Reststelsel
2
6Polish (pl)
Zredukowany układ reszt modulo
0
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
نظام بواقي مصغر
enEnglish
Reduced residue system
glGalician
Sistema reducido de residuos
huHungarian
Redukált maradékrendszer
nlDutch
Reststelsel
plPolish
Zredukowany układ reszt modulo

Popularity rank trends

Best Rank English:
#573196
03.2014
Global:
#908573
10.2020

AI rank trends

Best Rank English:
#147119
02.2012
Global:
#183589
10.2014

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Reduced residue system from Wikipedia articles about Eulers theorem, Modular arithmetic, Residue number system, Totative and Eulers totient function. Whereas reading the article about Reduced residue system people most often go to Wikipedia articles on Modular arithmetic, Eulers totient function, Multiplicative group of integers modulo n, Residue number system and Cyclic group.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 16 March 2026

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About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information