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Midy's theorem: Proof of Midy's theorem, Midy's theorem in other bases & Extended Midy's theorem

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period (sequence A028416 in the OEIS). If the period of the decimal representation of a/p is 2n, so that

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Midy's theorem topic overview

The analysis highlights Proof of Midy's theorem, Midy's theorem in other bases and Extended Midy's theorem as prominent areas in the source structure around Midy's theorem.

Related topics: 18
Source areas: 4
Connected nodes: 22
Extracted relationships: 16
Concept neighborhoods: 10
Bridge connections: 22

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.

Overview · 10 topics

Proof of Midy's theorem · 4 topics

Midy's theorem in other bases · 3 topics

Extended Midy's theorem · 1 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.

Suggested research paths

A focused starting point derived from the topic graph, ranked independently of the source article order.

Start with these areas

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

Mathematics
French France
Mathematician
Decimal expansion
Fractions Fraction (mathematics)
Prime Prime number
Repeating decimal
Even Even number
OEIS On-Line Encyclopedia of Integer Sequences
9s complement Method of complements

Extended Midy's theorem

Divisor

Midy's theorem in other bases

Proof of Midy's theorem

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 Midy's theorem connects Entity context

The extracted context around Midy's theorem shows recurring relationship patterns in the source. For example, Midy's theorem → Dividing, For, If, Midy's, Similarly, The Another extracted example is Midy's theorem → However, Let, Midy's, Short, Suppose. Use these groups to spot repeated connection types before inspecting the individual relationships.

Midy's theorem

Top relations

related to Extended Midy's theorem · 6

Midy's theorem → Dividing, For, If, Midy's, Similarly, The

related to Proof of Midy's theorem · 5

Midy's theorem → However, Let, Midy's, Short, Suppose

related to External links · 3

Midy's theorem → Eric, MathWorld, Weisstein

related to Midy's theorem in other bases · 2

Midy's theorem → For, Midy's

Important terminology

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

Important terminology

displaystyle midy's theorem frac period base decimal overline bk -1 repeating multiple expansion dots 999 2n prime integer extended 19

Midy's theorem relationships Subject–Predicate–Object triples

TTTA extracted 16 structured relationships around Midy's theorem. Examples in this analysis include Midy's theorem → related to Extended Midy's theorem → If and Midy's theorem → related to Extended Midy's theorem → Midy's. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Midy's theorem	related to Extended Midy's theorem	If	0.60	section
Midy's theorem	related to Extended Midy's theorem	Midy's	0.60	section
Midy's theorem	related to Extended Midy's theorem	The	0.60	section
Midy's theorem	related to Extended Midy's theorem	For	0.60	section
Midy's theorem	related to Extended Midy's theorem	Dividing	0.60	section
Midy's theorem	related to Extended Midy's theorem	Similarly	0.60	section
Midy's theorem	related to External links	Weisstein	0.60	section
Midy's theorem	related to External links	Eric	0.60	section
Midy's theorem	related to External links	MathWorld	0.60	section
Midy's theorem	related to Midy's theorem in other bases	Midy's	0.60	section
Midy's theorem	related to Midy's theorem in other bases	For	0.60	section
Midy's theorem	related to Proof of Midy's theorem	Short	0.60	section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Midy's theorem bring nearby vocabulary together. In this analysis, examples include Midy's, Theorem and Extended. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Midy's theorem
- Midy's
- Theorem
- Extended
- Sum
- Displaystyle
- Decimal
- Expansion
- Base
- Numbers
- Portion
- Aligned
- Begin
midy's theorem
- Midy's
- Theorem
- Extended
- Sum
- Displaystyle
- Decimal
- Expansion
- Base
- Numbers
- Portion
- Aligned
- Begin
decimal expansion
- Expansion
- Repeating
- Numbers
- Portion
- Period
- Digits
- Extended
- Prime
- Midy's
- Theorem
- Base
- Overline
extended midy's theorem
- Midy's
- Theorem
- Sum
- Extended
- Displaystyle
- Base
- Decimal
- Expansion
- Multiple
- Numbers
- Portion
- Text
midy's theorem in other bases
- Midy's
- Theorem
- Extended
- Sum
- Displaystyle
- Decimal
- Expansion
- Base
- Numbers
- Portion
- Aligned
- Begin
proof of midy's theorem
- Midy's
- Theorem
- Extended
- Sum
- Displaystyle
- Decimal
- Expansion
- Base
- Numbers
- Portion
- Aligned
- Begin
base
- Displaystyle
- Bk
- Multiple
- Aligned
- Begin
- End
- Sum
- Dots
- Extended
- Integer
- Midy's
- Theorem
repeating decimal
- Expansion
- Repeating
- Numbers
- Portion
- Period
- Digits
- Extended
- Prime
- Midy's
- Theorem
- Base
- Multiple

Connections between topic areas Semantic bridges

For Midy's theorem, one of the stronger structural bridges in this analysis connects Midy's theorem with Overview. 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

Midy's theorem — Overview · splits 12 ⟂ 11

Midy's theorem — Proof of Midy's theorem · splits 18 ⟂ 5

Midy's theorem — Midy's theorem in other bases · splits 19 ⟂ 4

Map overview Semantic statistics

Midy's theorem

Nodes23

Edges22

Triples16

Avg. degree1.91

Density0.086957

Components1

Source & methodology

TTTA analyzes the structure around Midy's theorem to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Proof of Midy's theorem, Midy's theorem in other bases & Extended Midy's theorem, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Midy's theorem · EN edition · Analysis: TopicsToTalkAbout

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Midy's theorem topic overview

What this topic covers Research coverage

Key facts & relationships

Suggested research paths

Start with these areas

Proof of Midy's theorem

Midy's theorem in other bases

Extended Midy's theorem

Explore all related topics Closing gaps

Overview

Extended Midy's theorem

Midy's theorem in other bases

Proof of Midy's theorem

Advanced semantic analysis

How Midy's theorem connects Entity context

Midy's theorem

Top relations

Important terminology

Important terminology

Midy's theorem relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges

Map overview Semantic statistics

Midy's theorem

Source & methodology