Fermat cov lus qhia me ntsis

Hauv kev tshaj tawm no, peb yuav xav txog ib qho ntawm cov ntsiab lus tseem ceeb hauv txoj kev xav ntawm cov lej -  Fermat cov lus qhia me ntsismuaj npe tom qab Fabkis tus lej lej Pierre de Fermat. Peb tseem yuav tshuaj xyuas ib qho piv txwv ntawm kev daws qhov teeb meem los sib sau ua ke cov khoom uas tau nthuav tawm.

Nqe lus ntawm lub theorem

1. Thawj

If p yog tus naj npawb tseem ceeb a yog ib tug integer uas tsis divisible los ntawm pces a^p-1 - 1 muab faib los ntawm p.

Nws raug sau raws li nram no: a^p-1 ≡ 1 (tawm tsam p).

Nco ntsoov: Tus lej tseem ceeb yog tus lej ntuj uas tsuas yog faib los ntawm XNUMX thiab nws tus kheej yam tsis muaj seem.

Piv txwv li:

• a = 2
• p = 5
• a^p-1 - 1 = 2^{5 - 1} - 1 = 2⁴ – 1 = 16 – 1 = 15
• tooj 15 muab faib los ntawm 5 tsis muaj qhov seem.

2. Lwm txoj kev

If p yog tus lej tseem ceeb, a tej integer, ces a^p piv rau a module p.

a^p ≡ ib (tawm tsam p)

Keeb kwm ntawm kev nrhiav pov thawj

Pierre de Fermat tsim lub theorem hauv 1640, tab sis tsis tau ua pov thawj nws tus kheej. Tom qab ntawd, qhov no tau ua tiav los ntawm Gottfried Wilhelm Leibniz, German philosopher, logician, lej, thiab lwm yam. Nws ntseeg tau tias nws twb muaj pov thawj los ntawm 1683, txawm tias nws tsis tau luam tawm. Nws yog ib qho tseem ceeb uas Leibniz nrhiav tau lub theorem nws tus kheej, tsis paub tias nws twb tau tsim ua ntej lawm.

Thawj cov pov thawj ntawm lub theorem tau luam tawm nyob rau hauv 1736, thiab nws belongs rau Swiss, German thiab lej thiab kws kho tsheb, Leonhard Euler. Fermat's Little Theorem yog qhov tshwj xeeb ntawm Euler's theorem.

Piv txwv ntawm qhov teeb meem

Nrhiav qhov seem ntawm tus lej 2¹² on 12.

tshuaj

Cia peb xav txog tus lej 2¹² as 2⋅2¹¹.

11 yog tus lej tseem ceeb, yog li ntawd, los ntawm Fermat lub theorem me me peb tau txais:

2¹¹ ≡ 2 (tawm tsam 11).

Yog li, 2⋅2¹¹ ≡ 4 (tawm tsam 11).

Yog li tus lej 2¹² muab faib los ntawm 12 nrog rau qhov seem sib npaug 4.