Theorem yaing'ono ya Fermat

M'bukuli, tiwona imodzi mwamalingaliro akulu mu chiphunzitso cha integers -  Theorem yaing'ono ya FermatDzinali linachokera ku katswiri wa masamu wa ku France Pierre de Fermat. Tidzasanthulanso chitsanzo cha kuthetsa vutolo kuti tiphatikize mfundo zomwe zaperekedwa.

Chidziwitso cha theorem

1. Poyamba

If p ndi nambala yoyamba a ndi chiwerengero chomwe sichimagawidwa pndiye a^p-1 - 1 Ogawanika p.

Zalembedwa motere: a^p-1 ≡1 (motsutsa p).

Zindikirani: Nambala yayikulu ndi nambala yachilengedwe yomwe imangogawidwa ndi XNUMX ndipo palokha popanda kutsala.

Mwachitsanzo:

• a = 2
• p = 5
• a^p-1 - 1 = 2^{5 - 1} - 1 = 2⁴ 1 = 16 – 1 = 15
• nambala 15 Ogawanika 5 popanda chotsalira.

2. Njira ina

If p ndi nambala yayikulu, a chiwerengero chilichonse, ndiye a^p kufananiza ndi a modulo p.

a^p ≡ ndi (motsutsa p)

Mbiri yopeza umboni

Pierre de Fermat adapanga chiphunzitsocho mu 1640, koma sanadzitsimikizire yekha. Pambuyo pake, izi zinachitidwa ndi Gottfried Wilhelm Leibniz, wafilosofi wa ku Germany, woganiza bwino, wa masamu, ndi zina zotero. Amakhulupirira kuti anali ndi umboni kale ndi 1683, ngakhale kuti sunasindikizidwe. N'zochititsa chidwi kuti Leibniz anapeza theorem yekha, osadziwa kuti anali atapangidwa kale.

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.

Chitsanzo cha vuto

Pezani nambala yotsalira 2¹² on 12.

Anakonza

Tiyeni tiyerekeze nambala 2¹² as 2⋅2¹¹.

11 ndi nambala yayikulu, chifukwa chake, ndi theorem ya Fermat yomwe timapeza:

2¹¹ ≡2 (motsutsa 11).

Choncho, 2⋅2¹¹ ≡4 (motsutsa 11).

Ndiye nambala 2¹² Ogawanika 12 ndi chotsala chofanana ndi 4.