#numbertheory — Public Fediverse posts

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

GPT-6 Astra Max: Report on the decomposition into weight × level + jump in number theory

https://decompwlj.com/GTP6_Astra_decompwlj_number_theory_report_2026-09-05.html

#decompwlj #math #NumberTheory #AI #GPT6 #Astra #report

Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html

How to read this report

Primes VS Model A, the classic Cramér sequence

Twelve fingerprints

The complete status ledger

#math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html

How to read this report

Primes VS Model A, the classic Cramér sequence

Twelve fingerprints

The complete status ledger

#math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html

How to read this report

Primes VS Model A, the classic Cramér sequence

Twelve fingerprints

The complete status ledger

#math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html

How to read this report

Primes VS Model A, the classic Cramér sequence

Twelve fingerprints

The complete status ledger

#math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html

How to read this report

Primes VS Model A, the classic Cramér sequence

Twelve fingerprints

The complete status ledger

#math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

🎩🤓 Oh, joy! Yet another riveting tale of nerds with too much time on their hands, this time using a fleet of #Devins (whatever those are) to factor an obscenely large number because, why not? Who knew that playing with numbers could be so... thrilling? #RSA260 totally had it coming. 🧮💥
https://cognition.com/blog/factoring-rsa-260 #nerdsatplay #mathenthusiasts #numbertheory #thrilling #HackerNews #ngated

Alright, future engineers!

**Modulo Arithmetic:** The remainder after division.
Ex: `10 mod 3 = 1` (since `10 = 3*3 + 1`).
Pro-Tip: Super useful for clocks & cyclical patterns – it wraps around!

#DiscreteMath #NumberTheory #STEM #StudyNotes

Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193

Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192

References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190

Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189

Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188

Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187

Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186

Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185

Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184

Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183

Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182

Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181

Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180

Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178

Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177

Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176

Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices

t.me/scilib_yura15cbx/173

From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨

In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,

aᵖ ≡ a (mod p).

For example, when p = 5:
2⁵ − 2 = 30, which is divisible by 5, and
3⁵ − 3 = 240, which is also divisible by 5.

Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”

About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.

#Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge

This episode reinforces a recurring theme of the series: asymptotics is geometry in disguise. Whether through steepest descent, Laplace’s method, or contour deformation, the dominant contribution always comes from regions where analytic structure forces concentration. Learning to recognize these regions—and to justify why others do not contribute—is the real content of the method.
#NumberTheory #ComplexAnalysis #AnalyticNumberTheory #Mathematics #MathCommunity #STEM #PureMath
🔗 https://cortexdrifter.blogspot.com/2026/04/a-small-taste-from-my-new-book-season-2_25.html

Number theory was the one area of mathematics on which Pierre de Fermat (1607–65) worked throughout his life, and he found it ‘very beautiful and very subtle’.

Among other results, he said that the Polygonal Number Theorem (which asserts that every natural number is the sum of at most $n$ $n$-gonal numbers) was ‘a most beautiful and wholly general proposition […] this marvellous proposition’.

(He offered no proof of this result, but claimed to have one in a marginal note to Diophantus' Arithmetica; this was the same book in which he noted what became known as Fermat's Last Theorem.)

Fermat also seems to have counted magic squares and analogous configurations as part of number theory, and wrote that: ‘I know hardly anything more beautiful in arithmetic than these numbers that some call planetary and others magic’. (The term ‘planetary’ is derived from certain treatises linking the magic squares to planets used in talismans.)

He said he had found a rule to find magic cubes (one of his examples is in the attached image) and also determined how many different ways each such cube can be arranged, which he called ‘one of the most beautiful things in arithmetic’.

1/2

[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Fermat #NumberTheory #HistMath #MathematicalBeauty #MagicSquare

Why weren't you taught the cubic formula?
https://www.youtube.com/watch?v=N-KXStupwsc
#Mathologer #BurkardPolster @Mathologer
#NumberTheory #algebra #geometry
#quadratic #cubic #polynomial
#maths #mathematics #education
#math

Accessible proofs of the transcendence of e and pi:
https://www.youtube.com/watch?v=WyoH_vgiqXM
#maths #e #pi #transcendental #polynomial #number #numbertheory #Mathologer #math