Китайская гипотеза

Китайская гипотеза — опровергнутая гипотеза, что целое число является простым тогда и только тогда, когда делится на ; другими словами, что целое просто тогда и только тогда, когда . В одну сторону утверждение истинно, а именно, что когда  — простое, то (это специальный случай малой теоремы Ферма). Однако обратное утверждение, что из следует простота , неверно, а потому и в целом гипотеза не верна. Наименьшим контрпримером является число . Составные числа , для которых делится на , называются числами Пуле. Они являются частным случаем псевдопростых чисел Ферма.

Выдвинута XIX веке в работе математика Ли Шань-Ланя (кит. 李善兰; 1811—1882) времён империи Цин[1]. Ли Шань-Лань впоследствии осознал ошибочность утверждения и изъял его из всех последующих работ, но несмотря на это утверждение стало распространяться под его именем[1]. В результате ошибки перевода в 1898 году гипотеза была приписана времени Конфуция и с тех пор иногда ошибочно считается древнекитайской[1][2].

Примечания

  1. ↑ 1 2 3 Ribenboim, 2006, с. 88–89.
  2. ↑ Needham, 1959, с. 54.

Литература

  • Paulo Ribenboim. The Little Book of Bigger Primes. — Springer Science & Business Media, 2006. — С. 88–89. — ISBN 9780387218205.
  • Joseph Needham, In collaboration with Wang Ling. Science and Civilisation in China. — Cambridge, England: Cambridge University Press, 1959. — Т. 3: Mathematics and the Sciences of the Heavens and the Earth. — С. 54.
  • Leonard Eugene Dickson. History of the Theory of Numbers. — New York: Dover, 2005. — Т. 1: Divisibility and Primality. — ISBN 0-486-44232-2.
  • Paul Erdős. On the Converse of Fermat's Theorem // American Mathematical Monthly. — 1949. — Т. 56, вып. 9. — С. 623–624. — doi:10.2307/2304732.
  • Ross Honsberger. An Old Chinese Theorem and Pierre de Fermat // Mathematical Gems. — Washington, DC: Math. Assoc. Amer., 1973. — Т. I. — С. 1–9.
  • James Hopwood Jeans. The converse of Fermat's theorem // Messenger of Mathematics. — 1898. — Т. 27. — С. 174.
  • Joseph Needham. Ch. 19 // Science and Civilisation in China, Vol. 3: Mathematics and the Sciences of the Heavens and the Earth. — Cambridge, England: Cambridge University Press, 1959.
  • Han Qi. Transmission of Western Mathematics during the Kangxi Kingdom and Its Influence Over Chinese Mathematics. — Beijing: Ph.D. thesis, 1991.
  • Paulo Ribenboim. The New Book of Prime Number Records. — New York: Springer-Verlag, 1996. — С. 103–105. — ISBN 0-387-94457-5.
  • Daniel Shanks. Solved and Unsolved Problems in Number Theory. — New York: Chelsea, 1993. — С. 19–20. — ISBN 0-8284-1297-9.
  • Li Yan, Du Shiran. Chinese Mathematics: A Concise History / Translated by John N. Crossley and Anthony W.-C. Lun. — Oxford, England, 1987. — ISBN 0-19-858181-5.

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