amanani agqibeleleyo

IMathematika ibikho ukususela ekuqaleni. Ukuba ukufunyanwa kwethambo le-Ishango (ngaphezu kweminyaka engama-20.000 eyadlulayo) kuya kukholelwa, inokuba bubungqina bokuqala bolwazi lwamanani okuqala kunye nokuphindaphinda, kodwa isihloko sihlala siphikisana. Ngelixa izibalo zihlala ziyimfihlakalo kuninzi lwethu, zibonwa ngabanye njengendlela enkulu yokuqonda kunye nokuhlalutya ihlabathi. Kwimathematika kukho amanani agqibeleleyoInto abantu abaninzi abangayaziyo.

Kweli nqaku siza kukuxelela yonke into oyifunayo ukuyazi ngamanani agqibeleleyo kunye neempawu zabo.

yintoni amanani agqibeleleyo

Amanani agqibeleleyo amalunga nokufumana iiprimes zeMersenne. Enyanisweni, iProposition 36 yeNcwadi IX yeEuclid's Elements ithi ukuba iMersenne inombolo 2n – 1 yiprime, ngoko ke u-2n-1 (2n – 1) linani eligqibeleleyo.

URené Descartes uqinisekisile kwileta eya kuMason ukuba naliphi na inani lalingu-Euclid, kodwa akazange ayingqine ithiyori yakhe. Endaweni yoko, ingcali yezibalo yaseSwitzerland uLeonhard Euler Wayengowokuqala ukubonisa iCartesian observation. Ukudityaniswa kweziphumo ze-Euclid kunye ne-Euler kuvumela ukufumana uphawu olupheleleyo lwamanani agqibeleleyo.

Amanani amane okuqala agqibeleleyo aye aziwa ukususela kumaxesha amandulo. Zivela kwimisebenzi kaNico Marcos de Graça kunye noTheon de Smyrna. Inombolo yesihlanu egqibeleleyo ikhankanywe kwiKhowudi yesiLatini ye-1456. Inombolo yesithandathu neyesixhenxe egqibeleleyo yafunyanwa yiCataldi ngekhulu le-XNUMX. yaza eyesibhozo yaba nguEuler ngowe-1772.

Ke ekuqaleni koo-1950 sasisazi amanani apheleleyo angama-12, kodwa ke sibulela kwi-GIMPS (i-Intanethi enkulu ye-Mersenne Prime Search), ukukhangela kwakhawuleza ngobuchwephesha obuninzi kunye nokusetyenziswa kweekhompyuter kwi-1990s.

Zenzelwe ntoni

Ukuba iingcali zemathematika ezininzi zijonga amanani aphambili njengesiseko se-arithmetic, ngoko ke amanani agqibeleleyo akasebenzisi nto, kuba azisetyenziswanga ukusombulula iiequations, factor okanye ukungena kwindawo yecryptography.

Kumaxesha amandulo, babegqalwa njengabongamileyo, yaye omnye wabona indima engaqondakaliyo kuyo: “Isithandathu ngokwaso silinani eligqibeleleyo, kungekhona ngenxa yokuba uThixo wadala yonke into ngeentsuku ezintandathu, kodwa ngenxa yokuba uThixo wadala yonke into ngeentsuku ezintandathu ngenxa yokuba inani ligqibelele” – INgcwele uAugustine kwisiXeko sikaThixo (420 AD)

Zezinye zeemfihlelo zemathematika, kwaye ukukhangela amanani amatsha agqibeleleyo kuyaqhubeka kutsala umdla weengcali zezibalo ezininzi.

Kukho uqikelelo oluninzi malunga namanani agqibeleleyo. Intelekelelo ngumgaqo ongazange ungqinwe. Nazi ezintathu:

• Amanani agqibeleleyo kaEuclid onke ngamanani alinganayo kuba enye yezinto ngamandla ka-2. Kodwa akukho bungqina bubonisa ukuba akukho manani angaqhelekanga agqibeleleyo;
• Onke amanani agqibeleleyo aziwayo aphela ngo-6 okanye ku-28, kodwa oku akusoloko kunjalo;
• Kwaye akuzange kungqinwe ukuba ngokwenene kukho amanani amaninzi ngokungenasiphelo.

athini amanani agqibeleleyo

Amanani agqibeleleyo anqabile. Ngelixa zonke iingcali zezibalo zivuma ukuba kukho inani elingenasiphelo lazo (elingazange lingqinwe), namhlanje sazi kuphela ama-50 kwaye asinakuqiniseka ukuba akukho nani lithetha ngokugqibeleleyo elingafunyaniswanga ukusukela kuma-47.

Inombolo yokugqibela egqibeleleyo yafunyanwa ngoJanuwari 2018. Ukufunyanwa kwenkulumbuso entsha enkulu kakhulu kuthetha ukufunyanwa kwenani elitsha eligqibeleleyo, elikufunyanwa kwenombolo 2⁷⁷²³²⁹¹⁷-1.

Kukho amanani amathathu kuphela agqibeleleyo angaphantsi kwe-1000: 6, 28 kunye no-496. Ngokucacileyo namanani agqibeleleyo aphela ngo-6 okanye u-8, nangona oku kungazange kungqinwe, akusoloko kunjalo.

Amanani agqibeleleyo kwifomula 2n-1 (2n - 1) ngamanani angama-triangular (okanye anehexagonal). Kwelinye icala, onke amanani alinganayo ngaphandle kwelokuqala ngokugqibeleleyo inani elilinganayo lisisixa sika 2(n-1)/2 iityhubhu zamanani odd okuqala. Umzekelo:

• 28 = 1³+ 3³,
• 496 = 1³+ 3³ + 5³ + 7³,
• 8128 = 1³+ 3³ + 5³ + 7³ + 9³ + 11³ + 13³ + 15³.

Amanani asibhozo okuqala agqibeleleyo ngala:

• 6
• 28
• 496
• 8128
• 336
• 869.056
• 691.328
• 2 305 843 008 139 952 128.

Imbali ethile

Ongcwele uAugustine, owaziwa ngokuba nguAugustine waseHippo (354-430), fWayesisithandi sobulumko saseRoma, umbhali, ingcali yezibalo nomfundisi. Ukuba uwufundile umxholo wentanda-bulumko, igama liya kuqheleka kuwe, kuba engomnye weentanda-bulumko ezidla ngokuwufunda lo mbandela. Njengezinye iinkcuba-buchopho ezininzi zexesha lakhe, uSaint Augustine wayengomnye wabo baphuhlisayo baza benza nzulu ulwazi kwiinkalo ezisusela kwifilosofi ukuya kwizibalo, kuninzi esikubonayo kunokuba sinokucinga namhlanje.

Kaloku, uAugustine waseHippo wathi amanani agqibeleleyo anesizathu sokubakho. Kwincwadi yakhe ethi The City of God, wachaza ukuba u-6 ugqibelele kuba uThixo wadala ihlabathi ngeentsuku ezintandathu. Inani elilandelayo, 28, lihambelana nenani leentsuku ezithathayo ukuze iNyanga ijikeleze umhlaba kube kanye. Le ngxelo ayikho ngaphandle kwengxabano, i-coincidence okanye akunjalo?

Akukho ngcaciso inikwayo ngamanani amabini alandelayo. Bangama-496 kunye nama-8128. Amanani amane okuqala afunyanwa kwangenkulungwane yokuqala ye-AD nguNicomachus waseGerasa, intanda-bulumko kunye nesazi sezibalo owayehlala kwisixeko sakudala saseDekapoli, ngoku iJordan, eyayiyeyaseBukhosi baseRoma.

Ukufumana inani lesihlanu eligqibeleleyo kuye kwafuneka ukuba sithathe umtsi omkhulu kwimbali de sifike kwinkulungwane yeshumi elinesihlanu, ekubeni inani lesihlanu eligqibeleleyo 33 550 336 livele kwimibhalo-ngqangi ukusuka kule nkulungwane. Eyesithandathu neyesixhenxe, ezizi-8.589.869.056 137.438.691.328 1588 XNUMX nezili-XNUMX XNUMX XNUMX XNUMX zafunyanwa kwinkulungwane kamva, ngowe-XNUMX, yingcali yezibalo yaseItali uPietro Cataldi.

Njengamanani agqibeleleyo, kuphela inani eliqingqiweyo lamanani e-Mersenne aziwayo. Amanani athiywa ngoMarin Mason, indoda eyabhenca uthotho lweengcamango malunga nabo. UMason wayesisithandi sobulumko saseFransi, ingcali yezibalo, nomfundisi (1588-1648).

Ngu-Euler owafumanisa la manani akhethekileyo, ngenxa yesiseko esibekwe nguMason. ULeonhard Paul Euler (1707-1783) wayeyingcali yezibalo yaseSwitzerland kunye nefiziksi. Ewe, igama lakhe liya kuba sele liqhelekile kuwe, kuba ukufumana inombolo yesibhozo egqibeleleyo yayingeyompumelelo yakhe kuphela. Ikwafumene igama layo kwinombolo kaEuler (e), esetyenziswa kwiifomyula ezininzi zomzimba kunye nezokubala.

Ndiyathemba ukuba ngolu lwazi unokufunda ngakumbi malunga nala manani kunye neempawu zabo.