#modulararithmetic — Public Fediverse posts

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

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

🔒🧠 "Understanding" ECDSA: Because nothing screams 'security' like a tangled mess of modular arithmetic and a cameo from Fibonacci. Who knew deciphering digital signatures required a PhD in cryptic-ology? 😂🔍
https://avidthinker.github.io/2025/11/28/understanding-ecdsa/ #ECDSA #Understanding #Cryptography #DigitalSignatures #ModularArithmetic #HackerNews #ngated

🔒🧠 "Understanding" ECDSA: Because nothing screams 'security' like a tangled mess of modular arithmetic and a cameo from Fibonacci. Who knew deciphering digital signatures required a PhD in cryptic-ology? 😂🔍
https://avidthinker.github.io/2025/11/28/understanding-ecdsa/ #ECDSA #Understanding #Cryptography #DigitalSignatures #ModularArithmetic #HackerNews #ngated

Terrible accident in Rome.
2 police patrol cars engaged in different crime operations, both driving at full speed and with their sirens blaring, crashed at an intersection.

Probably each driver just heard their own siren but not the other's.

So, 2 overlapping concurrent alerts summed up to none.🤔

(It seems there could be a more general law to explain above event, but I'm not very sure what it is)

#modulararithmetic #warnings #selfalert

New video on solving an RPG puzzle with #JuliaLang

https://youtu.be/L4QgBuiMmUk

#julialang #modulararithmetic #linearalgebra #rpg

How to decrypt c when e is not co-prime with phi(n) and e is non-prime

https://crypto.stackexchange.com/questions/103830/how-to-decrypt-c-when-e-is-not-co-prime-with-phin-and-e-is-non-prime

#modulararithmetic #publickey #rsa

How to decrypt c when e is not co-prime with phi(n) and e is non-prime

https://crypto.stackexchange.com/questions/103830/how-to-decrypt-c-when-e-is-not-co-prime-with-phin-and-e-is-non-prime

#modulararithmetic #publickey #rsa

Must RSA exponent and modulus be odd

https://crypto.stackexchange.com/questions/103516/must-rsa-exponent-and-modulus-be-odd

#modulararithmetic #rsa

Must RSA exponent and modulus be odd

https://crypto.stackexchange.com/questions/103516/must-rsa-exponent-and-modulus-be-odd

#modulararithmetic #rsa