Fermat's obere theorem

N'akwụkwọ a, anyị ga-atụle otu n'ime ihe ndị bụ isi na tiori nke integers -  Fermat's obere theoremAha ya bụ onye France mathematician bụ Pierre de Fermat. Anyị ga-enyochakwa ihe atụ nke idozi nsogbu ahụ iji mee ka ihe a na-egosi sie ike.

Nkwupụta nke theorem

1. Mmalite

If p bụ nọmba mbụ a bụ integer na-adịghị nkewa site pmgbe ahụ a^p-1 - 1 nkewa p.

Edere ya nke ọma dịka nke a: a^p-1 1 (imegide) p).

Cheta na: Ọnụọgụ mbụ bụ ọnụọgụ okike nke naanị XNUMX ga-ekewa na ya onwe ya na-enweghị ihe fọdụrụ.

Ọmụmaatụ:

• a = 2
• p = 5
• a^p-1 - 1 = 2^{5 - 1} - 1 = 2⁴ - 1 = 16 - 1 = 15
• ọnụ ọgụgụ 15 nkewa 5 na-enweghị nke fọdụrụ.

2. Ihe ozo

If p bụ nọmba ekwentị, a ọnụọgụ ọnụọgụ ọ bụla, yabụ a^p iji tụnyere a modulo p.

a^p ≡ a (imegide) p)

Akụkọ ihe mere eme nke ịchọta ihe akaebe

Pierre de Fermat chepụtara usoro mmụta ahụ na 1640, mana o gosipụtaghị ya n'onwe ya. Ka oge na-aga, nke a bụ Gottfried Wilhelm Leibniz, onye ọkà ihe ọmụma German, onye ọkà mmụta mgbakọ na mwepụ, wdg. A kwenyere na o nweworị ihe akaebe ahụ na 1683, ọ bụ ezie na ọ dịghị mgbe e bipụtara ya. Ọ bụ ihe kwesịrị ịrịba ama na Leibniz chọtara theorem n'onwe ya, n'amaghị na e chepụtala ya na mbụ.

The first proof of the theorem was published in 1736, and it belongs to the Swiss, German and mathematician and mechanic, Leonhard Euler. Fermat’s Little Theorem is a special case of Euler’s theorem.

Ọmụmaatụ nke nsogbu

Chọta nọmba fọdụrụnụ 2¹² on 12.

ngwọta

Ka anyị were ya na nọmba 2¹² as 2⋅2¹¹.

11 bụ nọmba mbụ, yabụ, site na obere usoro ọmụmụ Fermat anyị nwetara:

2¹¹ 2 (imegide) 11).

N'ihi ya, 2⋅2¹¹ 4 (imegide) 11).

Ya mere, nọmba 2¹² nkewa 12 ya na nke fọduru ya 4.