History
Pierre de Fermat first stated the theorem in a letter dated October 18, 1640, to his friend and confidant Frénicle de Bessy as the following: p divides a p−1 − 1 whenever p is prime and a is coprime to p.
As usual, Fermat did not prove his assertion, only stating:
Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je n'appréhendois d'être trop long.
(And this proposition is generally true for all progressions and for all prime numbers; the proof of which I would send to you, if I were not afraid to be too long.)
Euler first published a proof in 1736 in a paper entitled "Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio", but Leibniz left virtually the same proof in an unpublished manuscript from sometime before 1683.
The term "Fermat's Little Theorem" was first used in 1913 in Zahlentheorie by Kurt Hensel:
Für jede endliche Gruppe besteht nun ein Fundamentalsatz, welcher der kleine Fermatsche Satz genannt zu werden pflegt, weil ein ganz spezieller Teil desselben zuerst von Fermat bewiesen worden ist."
(There is a fundamental theorem holding in every finite group, usually called Fermat's little Theorem because Fermat was the first to have proved a very special part of it.)
It was first used in English in an article by Irving Kaplansky, "Lucas's Tests for Mersenne Numbers," American Mathematical Monthly, 52 (Apr., 1945).
Read more about this topic: Fermat's Little Theorem
Famous quotes containing the word history:
“The second day of July 1776, will be the most memorable epoch in the history of America. I am apt to believe that it will be celebrated by succeeding generations as the great anniversary festival. It ought to be commemorated, as the day of deliverance, by solemn acts of devotion to God Almighty. It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires and illuminations, from one end of this continent to the other, from this time forward forever more”
—John Adams (1735–1826)
“The history is always the same the product is always different and the history interests more than the product. More, that is, more. Yes. But if the product was not different the history which is the same would not be more interesting.”
—Gertrude Stein (1874–1946)
“The steps toward the emancipation of women are first intellectual, then industrial, lastly legal and political. Great strides in the first two of these stages already have been made of millions of women who do not yet perceive that it is surely carrying them towards the last.”
—Ellen Battelle Dietrick, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 13, by Susan B. Anthony and Ida Husted Harper (1902)