Abc conjecture

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Abc conjecture topic overview

The analysis highlights Consequences, Claimed proofs and Formulations as prominent areas in the source structure around Abc conjecture.

Related topics: 67
Source areas: 8
Connected nodes: 75
Extracted relationships: 113
Concept neighborhoods: 42
Bridge connections: 75

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.

Consequences · 29 topics

Overview · 12 topics

Claimed proofs · 9 topics

Formulations · 5 topics

Theoretical results · 4 topics

Computational results · 3 topics

Refined forms, generalizations and related statements · 3 topics

Examples of triples with small radical · 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.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Conjectured by: Joseph Oesterlé · David Masser
Conjectured in: 1985
Consequences: Beal conjecture · Erdős–Ulam problem · Faltings' theorem · Fermat's Last Theorem · Fermat–Catalan conjecture
Equivalent to: Modified Szpiro conjecture
Field: Number theory

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

Formulations

Examples of triples with small radical

Fermat's little theorem
Lando & Zvonkin 2004 Abc conjecture

Consequences

Conditional proof
Roth's theorem
Diophantine approximation
Algebraic numbers Algebraic number
Mordell conjecture Faltings' theorem
Gerd Faltings
Vojta's conjecture
Erdős–Woods conjecture Erdős–Woods number
Wieferich primes Wieferich prime
Marshall Hall's conjecture
Fermat's Last Theorem
A famously difficult proof by Andrew Wiles Wiles's proof of Fermat's Last Theorem
Lim sup Limit superior and limit inferior
Fermat–Catalan conjecture
L-function Dirichlet L-function
Legendre symbol
Siegel zero
Number fields Number field
Polynomial
Perfect powers
Integers
Simple zeros Simple zero
Tijdeman's theorem
The Diophantine equation n! + A = k2 Brocard's problem
Beal conjecture
Lang's conjecture Néron–Tate height
Height Height function
Erdős–Ulam problem
Siegel's theorem about integral points on algebraic curves Siegel's theorem on integral points

Theoretical results

Bounded above Upper bound
Exponential Exponential function
Constants Constant (mathematics)
Effectively computable

Computational results

Refined forms, generalizations and related statements

Claimed proofs

Lucien Szpiro
Inter-universal Teichmüller theory
Peter Scholze
Jakob Stix
Kyoto Kyoto University
The Kyoto research institute Research Institute for Mathematical Sciences
Kiran Kedlaya
Edward Frenkel
Nature Nature (journal)

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 Abc conjecture connects Entity context

The extracted context around Abc conjecture shows recurring relationship patterns in the source. For example, Abc conjecture → All, An, Andrew Wiles, As, Ax, Aym, Bxn, By, Catalan, Cz, Diophantine, Dąbrowski, Erdős, Euclidean, Fermat's Last Theorem, Gerd Faltings, Granville, However, Lang's, Langevin Another extracted example is Abc conjecture → ABC, ABC's, ABC-Conjecture, Abderrahmane Nitaj's ABC, Barry MazurPhilosophy, Brian Hayes, Conjecture, Conjecture Numberphile, Distributed, Easy, ElkiesQuestions, Eric, Home, IUT, MathOverflowABC Conjecture Polymath, MathWorld, Mochizuki, Mochizuki's, Noam, Number Archived. Use these groups to spot repeated connection types before inspecting the individual relationships.

Top relations

related to Consequences · 40

Abc conjecture → All, An, Andrew Wiles, As, Ax, Aym, Bxn, By, Catalan, Cz, Diophantine, Dąbrowski, Erdős, Euclidean, Fermat's Last Theorem, Gerd Faltings, Granville, However, Lang's, Langevin

related to External links · 24

Abc conjecture → ABC, ABC's, ABC-Conjecture, Abderrahmane Nitaj's ABC, Barry MazurPhilosophy, Brian Hayes, Conjecture, Conjecture Numberphile, Distributed, Easy, ElkiesQuestions, Eric, Home, IUT, MathOverflowABC Conjecture Polymath, MathWorld, Mochizuki, Mochizuki's, Noam, Number Archived

related to Claimed proofs · 10

Abc conjecture → Although, He, IUTT, Lucien Szpiro, Shinichi Mochizuki, Since August, Szpiro's, Teichmüller, The, This

related to Computational results · 10

Abc conjecture → ABC, Although, As, Dutch Kennislink, Home, In, Leiden University, Mathematics Department, May, Netherlands

Consequences · 7

Abc conjecture → Beal conjecture, Erdős–Ulam problem, Faltings' theorem, Fermat's Last Theorem, Fermat–Catalan conjecture, Roth's theorem, Tijdeman's theorem

related to Theoretical results · 7

Abc conjecture → Bounds, In, K1, K2, K3, Specifically, The

related to Formulations · 5

Abc conjecture → Before, For, If, Specifically, The

related to Refined forms, generalizations and related statements · 4

Abc conjecture → Baker, Mason, Stothers, The

Conjectured by · 2

Abc conjecture → David Masser, Joseph Oesterlé

Conjectured in · 1

Abc conjecture → 1985

Important terminology

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

Important terminology

conjecture abc integers number proof displaystyle rad triples theorem theory prime many positive mochizuki claimed equivalent szpiro radical also fermat's

Abc conjecture relationships Subject–Predicate–Object triples

TTTA extracted 113 structured relationships around Abc conjecture. Examples in this analysis include Abc conjecture → Conjectured by → Joseph Oesterlé and Abc conjecture → Conjectured by → David Masser. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Abc conjecture	Conjectured by	Joseph Oesterlé	1.00	infobox
Abc conjecture	Conjectured by	David Masser	1.00	infobox
Abc conjecture	Conjectured in	1985	1.00	infobox
Abc conjecture	Consequences	Beal conjecture	1.00	infobox
Abc conjecture	Consequences	Erdős–Ulam problem	1.00	infobox
Abc conjecture	Consequences	Faltings' theorem	1.00	infobox
Abc conjecture	Consequences	Fermat's Last Theorem	1.00	infobox
Abc conjecture	Consequences	Fermat–Catalan conjecture	1.00	infobox
Abc conjecture	Consequences	Roth's theorem	1.00	infobox
Abc conjecture	Consequences	Tijdeman's theorem	1.00	infobox
Abc conjecture	Equivalent to	Modified Szpiro conjecture	1.00	infobox
Abc conjecture	Field	Number theory	1.00	infobox
Abc conjecture	is a	integer analogue of the Mason	0.90	text

Related concept clusters Concept neighborhoods

The concept neighborhoods around Abc conjecture bring nearby vocabulary together. In this analysis, examples include Conjecture, Rad and Number. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Abc conjecture
- Conjecture
- Rad
- Number
- Theorem
- Theory
- Triples
- Version
- Displaystyle
- Integers
- Fermat's
- Last
- Bound
abc conjecture
- Conjecture
- Number
- Rad
- Integers
- Equivalent
- Theory
- Displaystyle
- Theorem
- Triples
- Bound
- Form
- Version
conjecture
- Number
- Integers
- Equivalent
- Theory
- Displaystyle
- Theorem
- Bound
- Form
- Rad
- Szpiro
- Version
- Fermat's
number theory
- Theory
- Triples
- Small
- Claimed
- Consequences
- Oesterlé
- Factors
- Proof
- Would
- Prime
- Modified
- Problem
positive integers
- Coprime
- Positive
- Prime
- Example
- Rad
- Equivalent
- Fermat's
- Form
- Last
- Displaystyle
- Many
- Theorem
prime factors
- Prime
- Integer
- Radical
- Small
- Consequences
- Masser
- Modified
- Oesterlé
- Problem
- Example
- Results
- Number
szpiro conjecture
- Number
- Rad
- Integers
- Problem
- Equivalent
- Theory
- Displaystyle
- Theorem
- Bound
- Form
- Integer
- Would
radical of an integer
- Small
- Results
- Integer
- Radical
- Theorem
- Triples
- Consequences
- Masser
- Modified
- Oesterlé
- Problem
- Example

Connections between topic areas Semantic bridges

For Abc conjecture, one of the stronger structural bridges in this analysis connects Abc conjecture with Consequences. 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

Abc conjecture — Consequences · splits 46 ⟂ 30

Abc conjecture — Overview · splits 63 ⟂ 13

Abc conjecture — Claimed proofs · splits 66 ⟂ 10

Abc conjecture — Formulations · splits 70 ⟂ 6

Abc conjecture — Theoretical results · splits 71 ⟂ 5

Abc conjecture — Computational results · splits 72 ⟂ 4

Abc conjecture — Refined forms, generalizations and related statements · splits 72 ⟂ 4

Abc conjecture — Examples of triples with small radical · splits 73 ⟂ 3

Map overview Semantic statistics

Abc conjecture

Nodes76

Edges75

Triples113

Avg. degree1.97

Density0.026316

Components1

Source & methodology

TTTA analyzes the structure around Abc conjecture to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Consequences, Claimed proofs & Formulations, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Abc conjecture · EN edition · Analysis: TopicsToTalkAbout