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Automorphic number: Definition and properties, Extensions & Overview

In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose square "ends" in the same digits as the number itself.

Language: English [EN]
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Automorphic number topic overview

The analysis highlights Definition and properties, Extensions and Overview as prominent areas in the source structure around Automorphic number.

Related topics
21
Source areas
3
Connected nodes
24
Extracted relationships
17
Concept neighborhoods
18
Bridge connections
24

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Definition and properties · 15 topics
Overview · 4 topics
Extensions · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition and properties

Extensions

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Automorphic number connects Entity context

The extracted context around Automorphic number shows recurring relationship patterns in the source. For example, Automorphic number → Automorphic, Eric, MathWorld, Trimorphic Number, Weisstein Another extracted example is Automorphic number → An, For, Hensel's. Use these groups to spot repeated connection types before inspecting the individual relationships.

Automorphic number

Top relations

related to External links · 5
Automorphic number → Automorphic, Eric, MathWorld, Trimorphic Number, Weisstein
related to a-automorphic numbers · 3
Automorphic number → An, For, Hensel's
related to Definition and properties · 3
Automorphic number → As, For, Given
related to Trimorphic numbers · 3
Automorphic number → All, For, The
related to Extensions · 2
Automorphic number → Automorphic, These
related to References · 1
Automorphic number → PlanetMath

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle numbers automorphic base fixed number points function trimorphic ring polynomial mathbb -adic 10 -x given digits example integers modulo

Automorphic number relationships Subject–Predicate–Object triples

TTTA extracted 17 structured relationships around Automorphic number. Examples in this analysis include Automorphic number → related to a-automorphic numbers → An and Automorphic number → related to a-automorphic numbers → For. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Automorphic numberrelated to a-automorphic numbersAn0.60section
Automorphic numberrelated to a-automorphic numbersFor0.60section
Automorphic numberrelated to a-automorphic numbersHensel's0.60section
Automorphic numberrelated to Definition and propertiesGiven0.60section
Automorphic numberrelated to Definition and propertiesAs0.60section
Automorphic numberrelated to Definition and propertiesFor0.60section
Automorphic numberrelated to ExtensionsAutomorphic0.60section
Automorphic numberrelated to ExtensionsThese0.60section
Automorphic numberrelated to External linksWeisstein0.60section
Automorphic numberrelated to External linksEric0.60section
Automorphic numberrelated to External linksAutomorphic0.60section
Automorphic numberrelated to External linksMathWorld0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Automorphic number bring nearby vocabulary together. In this analysis, examples include Numbers, Base and Displaystyle. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Automorphic number
    • Numbers
    • Base
    • Displaystyle
    • Digits
    • Fixed
    • Modulo
    • Points
    • Natural
    • Number
    • Example
    • Given
    • Integers
  • automorphic number
    • Numbers
    • Trimorphic
    • Base
    • Function
    • Displaystyle
    • Digits
    • Polynomial
    • Fixed
    • Whose
    • Example
    • Integers
    • Modulo
  • natural number
    • Square
    • Trimorphic
    • Function
    • Point
    • Whose
    • Polynomial
    • Example
    • Integers
    • Modulo
    • Number
    • Mathbb
    • Ring
  • number base
    • Displaystyle
    • Numbers
    • Trimorphic
    • Fixed
    • Digits
    • Example
    • Function
    • Given
    • Points
    • Number
    • Polynomial
    • 10-adic
  • fixed point
    • Points
    • Numbers
    • Zero
    • Function
    • Thus
    • -adic
    • Mathbb
    • Ring
    • Polynomial
    • -x
    • 10-adic
    • Inverse
  • b {\displaystyle b} -adic
    • Fixed
    • Numbers
    • Points
    • Function
    • Ring
    • Number
    • Polynomial
    • -adic
    • -x
    • Displaystyle
    • Mathbb
    • Inverse
  • base 10
    • Displaystyle
    • Numbers
    • Fixed
    • Digits
    • Example
    • Given
    • Points
    • Number
    • 10-adic
    • Natural
    • Zero-divisor
    • Thus
  • prime omega function
    • Polynomial
    • Distinct
    • Thus
    • Zeroes
    • Modulo
    • Ring
    • Number
    • Point
    • Integers
    • -x
    • Mathbb
    • Points

Connections between topic areas Semantic bridges

For Automorphic number, one of the stronger structural bridges in this analysis connects Automorphic number with Definition and properties. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Automorphic numberDefinition and properties · splits 9 ⟂ 16
Automorphic numberOverview · splits 20 ⟂ 5
Automorphic numberExtensions · splits 22 ⟂ 3

Map overview Semantic statistics

Automorphic number

Nodes25
Edges24
Triples17
Avg. degree1.92
Density0.08
Components1

Source & methodology

TTTA analyzes the structure around Automorphic number to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Definition and properties, Extensions & Overview, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Automorphic number · EN edition · Analysis: TopicsToTalkAbout

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