A cikin wannan ɗaba'ar, za mu yi la'akari da ɗaya daga cikin fitattun ka'idojin lissafi - Theorem na ƙarshe na Fermat, wanda ya karɓi sunansa don girmamawa ga masanin lissafin Faransa Pierre de Fermat, wanda ya ƙirƙira shi gabaɗaya a cikin 1637.
Bayanin ka'idar
Ga kowane lamba na halitta n> da 2 lissafin:
an + bn =cn
ba shi da mafita a cikin adadi marasa sifili a, b и c.
Tarihin gano shaida
Duk da sauƙin tsari na Fermat's Last Theorem a matakin sauƙi na lissafin makaranta, neman tabbacinsa ya ɗauki fiye da shekaru 350. Manyan masana ilmin lissafi da masu son yin hakan ne suka yi, shi ya sa ake ganin cewa ka’idar ita ce jagora a yawan hujjojin da ba daidai ba. Sakamakon haka, masanin lissafin Ingilishi da Ba'amurke Andrew John Wiles ya zama wanda ya tabbatar da hakan. Wannan ya faru a cikin 1994, kuma an buga sakamakon a 1995.
A baya a cikin karni na XNUMX, ƙoƙarin nemo shaida don n = 3 Abu Mahmud Hamid ibn al-Khizr al-Khojandi masanin lissafin Tajik ne kuma masanin falaki. Duk da haka, ayyukansa ba su wanzu ba har yau.
Fermat da kansa ya tabbatar da theorem kawai don n = 4, wanda ya haifar da wasu tambayoyi game da ko yana da wata hujja ta gaba ɗaya.
Har ila yau, hujja na theorem na daban-daban n ya ba da shawarar masanan lissafi masu zuwa:
- domin n = 3Mutane: Leonhard Euler (Swiss, Jamusanci da mathematician da makaniki) a 1770;
- domin n = 5Mutane: Johann Peter Gustav Lejeune Dirichlet (masanin lissafin Jamusanci) da Adrien Marie Legendre (masanin lissafin Faransa) a 1825;
- domin n = 7: Gabriel Lame (Masanin lissafi na Faransa, makaniki, likitan lissafi da injiniya);
- ga duk sauki n <100 (tare da yuwuwar ban da 37, 59, 67): Ernst Eduard Kummer (masanin lissafi na Jamus).