Skaidrės apie Pierre de Fermat

2 Proofs
What is a proof?
Fermat’s Little Theorem
Snell’s law
Fermat’s Last Theorem
What if...
3 Summary
4 Sources
Tomas B (VJG) The mythically disappearing proofs of Fermat December 10, 2020 2 / 14
Pierre de Fermat
Born in 1607 (10.31-12.06)
Worked as a lawyer, was a great
mathematician
Known as the father of infinitesimal
calculus
Made notable contributions to number
theory, differential calculus, analytic
geometry, probability and even optics
Died in 1655.01.12
Tomas B (VJG) The mythically disappearing proofs of Fermat December 10, 2020 3 / 14
Important discoveries
Fermat’s Little Theorem
Fermat’s principle
Infinitesimal calculus
Fermat’s Christmas Theorem!
Fermat’s Last Theorem
Tomas B (VJG) The mythically disappearing proofs of Fermat December 10, 2020 4 / 14
Definition
Proof - a lot of gibberish, ending with the acronym QED or a little square
(). Usually writter in LATEX(like these slides)
Tomas B (VJG) The mythically disappearing proofs of Fermat December 10, 2020 5 / 14
Fermat’s Little Theorem
This theorem states, that
∀a ∈ N and p ∈ P, ap−1 ≡ 1(mod p)
Extended by Leonhard Euler to
aϕ(n) ≡ 1(mod n)∀a, n ∈ N
Tomas B (VJG) The mythically disappearing proofs of Fermat December 10, 2020 6 / 14
Physics by Fermat
Fermat’s principle says "Light always follows the fastest possible path"
From which Snell’s law is derived:
sin θ1
sin θ2
=
n2
n1
The proof is trivial and left as an exercise to the reader
Tomas B (VJG) The mythically disappearing proofs of Fermat December 10, 2020 7 / 14
Fermat’s Last Theorem
The theorem states
∀x ∈...

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