#eulertheorem — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #eulertheorem, aggregated by home.social.
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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
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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