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Pierre de Fermat died on January 12, 1665, at Castres, in the present-day department of Tarn. [22] The oldest and most prestigious high school in Toulouse is named after him: the Lycée Pierre-de-Fermat. French sculptor Théophile Barrau made a marble statue named Hommage à Pierre Fermat as a tribute to Fermat, now at the Capitole de Toulouse.
If 2 k + 1 is prime and k > 0, then k itself must be a power of 2, [1] so 2 k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023 [update] , the only known Fermat primes are F 0 = 3 , F 1 = 5 , F 2 = 17 , F 3 = 257 , and F 4 = 65537 (sequence A019434 in the OEIS ).
Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam [1] (a Latin treatise circulated in France c. 1636 ) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus.
In projective space the Fermat cubic is given by w 3 + x 3 + y 3 + z 3 = 0. {\displaystyle w^{3}+x^{3}+y^{3}+z^{3}=0.} The 27 lines lying on the Fermat cubic are easy to describe explicitly: they are the 9 lines of the form ( w : aw : y : by ) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
For illustration, let n be factored into d and e, n = de. The general equation a n + b n = c n. implies that (a d, b d, c d) is a solution for the exponent e (a d) e + (b d) e = (c d) e. Thus, to prove that Fermat's equation has no solutions for n > 2, it would suffice to prove that it has no solutions for at least one prime factor of every n.
De Witte's treatment is more original than that description might suggest, although limited to two dimensions; it uses calculus of variations to show that Huygens' construction and Fermat's principle lead to the same differential equation for the ray path, and that in the case of Fermat's principle, the converse holds. De Witte also noted that ...
This is a list of things named after Pierre de Fermat, a French amateur mathematician. This list is incomplete ; you can help by adding missing items . ( December 2012 )
The Fermat prize was created in 1989 and is awarded once every two years in Toulouse by the Institut de Mathématiques de Toulouse. The amount of the Fermat prize has been fixed at 20,000 Euros for the twelfth edition (2011).