Ch\u00fang ta \u0111\u1ec1u bi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh x2 + y2 = z2c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m kh\u00e1c kh\u00f4ng.<\/p>\n\n\n\n
V\u00ed d\u1ee5 b\u1ed9 ba s\u1ed1 g\u1ecdi l\u00e0 b\u1ed9 s\u1ed1 tam gi\u00e1c th\u1eddi Trung Qu\u1ed1c c\u1ed5 \u0111\u1ea1i c\u00f3 c\u1ea1nh g\u00f3c vu\u00f4ng l\u00e0 3, 4, \u0111\u01b0\u1eddng huy\u1ec1n l\u00e0 5 l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh x = 3; y = 4, z = 5.<\/p>\n\n\n\n
V\u1ea5n \u0111\u1ec1 \u0111\u1eb7t ra l\u00e0 li\u1ec7u b\u00e0i to\u00e1n m\u1edf r\u1ed9ng xn + yn = zn khi n > 2 c\u00f3 nghi\u1ec7m kh\u00e1c 0 hay kh\u00f4ng? Nghi\u1ec7m kh\u00e1c 0 \u00fd n\u00f3i c\u1ea3 ba x, y, z \u0111\u1ec1u ph\u1ea3i kh\u00e1c 0. N\u1ebfu kh\u00f4ng ch\u1ec9 c\u1ea7n v\u00ed d\u1ee5 x = 0 th\u00ec y=z c\u00f3 th\u1ec3 nghi\u1ec7m \u0111\u00fang v\u1edbi b\u1ea5t k\u00ec s\u1ed1 nguy\u00ean n\u00e0o.<\/p>\n\n\n\n
Ferma, nh\u00e0 to\u00e1n h\u1ecdc Ph\u00e1p v\u00e0o th\u1ebf k\u1ec9 XVII \u0111\u00e3 t\u1eebng nghi\u00ean c\u1ee9u v\u1ea5n \u0111\u1ec1 n\u00e0y. Ferma l\u00e0 m\u1ed9t lu\u1eadt s\u01b0 n\u1ed5i ti\u1ebfng \u0111\u1ed3ng th\u1eddi l\u00e0 nh\u00e0 to\u00e1n h\u1ecdc. Tuy \u00f4ng ch\u01b0a h\u1ec1 \u0111\u01b0\u1ee3c h\u1ecdc m\u00f4n to\u00e1n m\u1ed9t c\u00e1ch ch\u00ednh quy nh\u01b0ng \u00f4ng c\u00f3 ni\u1ec1m ham th\u00edch to\u00e1n h\u1ecdc v\u00e0 c\u00f3 nh\u1eefng s\u00e1ng t\u1ea1o phi ph\u00e0m. Ferma c\u00f3 th\u00f3i quen l\u00e0 khi \u0111\u1ecdc s\u00e1ch \u00f4ng th\u01b0\u1eddng ghi nh\u1eefng nh\u1eadn x\u00e9t c\u1ee7a m\u00ecnh \u1edf b\u00ean l\u1ec1 v\u00e0 c\u00e1c ch\u1ed7 gi\u1ea5y tr\u1eafng trong s\u00e1ch. Khi \u00f4ng qua \u0111\u1eddi, con \u00f4ng \u0111\u00e3 xem l\u1ea1i c\u00e1c b\u00fat t\u00edch v\u00e0 th\u01b0 t\u1eeb c\u1ee7a cha \u0111\u1ec3 l\u1ea1i v\u00e0 t\u00ecm th\u1ea5y \u1edf m\u1ed9t g\u00f3c trang c\u00f3 ghi \u201cKh\u00f4ng th\u1ec3 m\u1ed9t s\u1ed1 m\u00e0 khi n\u00e2ng l\u00ean lu\u1ef9 th\u1eeba b\u1eadc ba l\u1ea1i b\u1eb1ng t\u1ed5ng lu\u1ef9 th\u1eeba b\u1eadc ba c\u1ee7a hai s\u1ed1 kh\u00e1c. Kh\u00f4ng c\u00f3 m\u1ed9t s\u1ed1 m\u00e0 lu\u1ef9 th\u1eeba b\u1eadc b\u1ed1n l\u1ea1i b\u1eb1ng t\u1ed5ng lu\u1ef9 th\u1eeba b\u1eadc b\u1ed1n c\u1ee7a hai s\u1ed1 kh\u00e1c. N\u00f3i chung kh\u00f4ng th\u1ec3 t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 m\u00e0 khi n\u00e2ng l\u00ean lu\u1ef9 th\u1eeba l\u1edbn h\u01a1n 2 l\u1ea1i b\u1eb1ng t\u1ed5ng lu\u1ef9 th\u1eeba c\u00f9ng b\u1eadc c\u1ee7a hai s\u1ed1 kh\u00e1c. T\u00f4i \u0111\u00e3 c\u00f3 m\u1ed9t ch\u1ee9ng minh \u0111\u1ea7y \u0111\u1ee7 v\u00e0 tuy\u1ec7t \u0111\u1eb9p v\u1ec1 m\u1ec7nh \u0111\u1ec1 n\u00e0y nh\u01b0ng ti\u1ebfc r\u1eb1ng kh\u00f4ng \u0111\u1ee7 ch\u1ed7 gi\u1ea5y tr\u1ed1ng \u0111\u1ec3 vi\u1ebft ra \u0111\u01b0\u1ee3c\u201d. Nh\u01b0 v\u1eady theo c\u00e1ch n\u00f3i c\u1ee7a Ferma th\u00ec ph\u01b0\u01a1ng tr\u00ecnh xn + yn = zn v\u1edbi n > 2 kh\u00f4ng c\u00f3 nghi\u1ec7m kh\u00e1c kh\u00f4ng. C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u01b0\u01a1ng th\u1eddi \u0111\u1ec1u tin Ferma c\u00f3 th\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c k\u1ebft lu\u1eadn n\u00e0y g\u1ecdi \u0111\u00f3 l\u00e0 \u201c\u0111\u1ecbnh l\u00ed Ferma l\u1edbn\u201d.<\/p>\n\n\n\n
Nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc c\u1ea9n th\u1eadn kh\u00f4ng ho\u00e0n to\u00e0n tin c\u1eady v\u00e0o c\u00e1c ghi ch\u00fa c\u1ee7a Ferma n\u00ean h\u1ecd h\u1ebft s\u1ee9c t\u00ecm hi\u1ec3u s\u00e2u h\u01a1n v\u00e0 mong t\u00ecm l\u1ea1i \u0111\u01b0\u1ee3c c\u00e1c \u201cch\u1ee9ng minh tuy\u1ec7t \u0111\u1eb9p v\u00e0 \u0111\u1ea7y \u0111\u1ee7 c\u1ee7a Ferma\u201d. Th\u1ebf nh\u01b0ng tr\u1ea3i qua 300 n\u0103m v\u1ea5n \u0111\u1ec1 t\u01b0\u1edfng nh\u01b0 \u0111\u01a1n gi\u1ea3n \u0111\u00e3 l\u00e0m \u0111i\u00ean \u0111\u1ea3o c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc ki\u1ec7t xu\u1ea5t trong \u0111\u00f3 c\u00f3 c\u1ea3 Euler, Dirichlet, Legendre, v.v\u2026 l\u00e0 nh\u1eefng ng\u01b0\u1eddi m\u00e0 t\u00ean tu\u1ed5i c\u1ee7a h\u1ecd \u0111\u00e3 l\u1eebng danh tr\u00ean c\u00e1c t\u00e1c ph\u1ea9m v\u1ec1 to\u00e1n h\u1ecdc. Nh\u01b0ng c\u00f4ng s\u1ee9c c\u1ee7a h\u1ecd b\u1ecf ra kh\u00f4ng ph\u1ea3i l\u00e0 v\u00f4 \u00edch. N\u0103m 1770, Euler ch\u1ee9ng minh v\u1edbi n =3 v\u00e0 n = 4, \u0111\u1ecbnh l\u00ed Ferma l\u00e0 \u0111\u00fang. N\u0103m 1825, Dirichler v\u00e0 Legendre ch\u1ee9ng minh v\u1edbi n = 5 th\u00ec k\u1ebft lu\u1eadn ch\u00ednh x\u00e1c.<\/p>\n\n\n\n
N\u0103m 1839, Lamay ch\u1ee9ng minh k\u1ebft lu\u1eadn \u0111\u00fang v\u1edbi n = 7. Khomol khi b\u1eaft \u0111\u1ea7u nghi\u00ean c\u1ee9u \u201cs\u1ed1 l\u00ed t\u01b0\u1edfng\u201d v\u00e0o n\u0103m 1874 \u0111\u00e3 ch\u1ee9ng minh tr\u1eeb c\u00e1c s\u1ed1 37, 59 v\u00e0 67 th\u00ec v\u1edbi c\u00e1c s\u1ed1 nh\u1ecf h\u01a1n 100 k\u1ebft lu\u1eadn c\u1ee7a Ferma l\u00e0 ch\u00ednh x\u00e1c\u2026 Cho \u0111\u1ebfn n\u0103m 1976, c\u00f3 ng\u01b0\u1eddi d\u00f9ng m\u00e1y t\u00ednh \u0111i\u1ec7n t\u1eed ch\u1ee9ng minh v\u1edbi n < 125.000 th\u00ec \u0111\u1ecbnh l\u00ed Ferma ho\u00e0n to\u00e0n \u0111\u00fang. Nh\u1eefng k\u1ebft qu\u1ea3 v\u1eeba n\u00eau \u0111\u00e3 c\u1ed5 v\u0169 m\u1ecdi ng\u01b0\u1eddi, nh\u01b0ng n\u1ebfu c\u1ee9 ti\u1ebfp t\u1ee5c theo \u0111\u00e0 n\u00e0y th\u00ec \u201c\u0111\u1ecbnh l\u00ed l\u1edbn Ferma\u201d v\u0129nh vi\u1ec5n kh\u00f4ng c\u00f3 c\u01a1 h\u1ed9i tr\u1edf th\u00e0nh m\u1ed9t \u0111\u1ecbnh l\u00ed th\u1ef1c th\u1ee5 b\u1edfi v\u00ec n l\u00e0 m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean v\u00f4 c\u00f9ng v\u00f4 t\u1eadn.<\/p>\n\n\n\n
Nh\u01b0ng \u0111\u1ebfn nh\u1eefng n\u0103m cu\u1ed1i th\u1ebf k\u1ec9 XX v\u1ea5n \u0111\u1ec1 \u0111\u00e3 c\u00f3 chuy\u1ec3n bi\u1ebfn c\u01a1 b\u1ea3n \u0111\u1ec3 \u0111\u1ebfn h\u1ed3i k\u1ebft th\u00fac. V\u00e0o th\u00e1ng 9-1994 nh\u00e0 to\u00e1n h\u1ecdc Anh Andrew Wiles \u0111\u00e3 ho\u00e0n to\u00e0n ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00ed Ferma v\u00e0 b\u01b0\u1edbc sang th\u1ebf k\u1ec9 XXI \u0111\u1ecbnh l\u00ed Ferma \u0111\u00e3 tr\u1edf th\u00e0nh m\u1ed9t \u0111\u1ecbnh l\u00ed th\u1ef1c th\u1ee5. Con \u0111\u01b0\u1eddng m\u00e0 c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc hi\u1ec7n \u0111\u1ea1i gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n kh\u00f4ng gi\u1ed1ng v\u1edbi con \u0111\u01b0\u1eddng c\u1ee7a b\u1ea3n th\u00e2n Ferma, Euler v\u00e0 c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc ki\u1ec7t xu\u1ea5t ti\u1ec1n b\u1ed1i kh\u00e1c. To\u00e1n h\u1ecdc hi\u1ec7n \u0111\u1ea1i \u0111\u00e3 c\u00f3 nhi\u1ec1u ph\u00e2n ng\u00e0nh (l\u00ed lu\u1eadn \u0111\u01b0\u1eddng elip, l\u00ed thuy\u1ebft m\u00f4 h\u00ecnh, l\u00ed thuy\u1ebft bi\u1ec3u di\u1ec5n Canbi v.v..) ph\u00e1t huy \u0111\u01b0\u1ee3c t\u00e1c d\u1ee5ng t\u1ed5ng h\u1ee3p v\u00e0 \u0111\u01b0a l\u00ed thuy\u1ebft s\u1ed1 h\u1ecdc \u0111\u1ebfn ch\u1ed7 cao si\u00eau nh\u1edd nh\u1eefng c\u1ed1ng hi\u1ebfn xu\u1ea5t s\u1eafc c\u1ee7a nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc. D\u00f9 c\u00f3 nh\u1eefng c\u1ed1ng hi\u1ebfn xu\u1ea5t s\u1eafc, nh\u01b0ng do v\u1ea5n \u0111\u1ec1 tu\u1ed5i t\u00e1c n\u00ean Wiles kh\u00f4ng \u0111\u01b0\u1ee3c H\u1ed9i ngh\u1ecb To\u00e1n h\u1ecdc Qu\u1ed1c t\u1ebf n\u0103m 1998 t\u1eb7ng gi\u1ea3i th\u01b0\u1edfng Fields, nh\u01b0ng \u0111\u00e3 \u0111\u1eb7c c\u00e1ch \u0111\u1ec3 \u00f4ng b\u00e1o c\u00e1o chuy\u00ean \u0111\u1ec1 trong h\u1ed9i ngh\u1ecb l\u1edbn. V\u00e0o bu\u1ed5i t\u1ed1i h\u00f4m \u0111\u00f3, nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 \u0111\u1ebfn h\u1ed9i tr\u01b0\u1eddng s\u1edbm h\u00e0ng gi\u1edd \u0111\u1ec1 ngh\u1ecb \u00f4ng b\u00e1o c\u00e1o.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00ed l\u1edbn Ferma \u0111\u00e3 c\u00f3 h\u1ed3i k\u1ebft c\u1ee5c. Trong qu\u00e1 tr\u00ecnh ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed l\u1edbn Ferma \u0111\u00e3 ph\u00e1t sinh nhi\u1ec1u t\u01b0 t\u01b0\u1edfng to\u00e1n h\u1ecdc v\u00e0 c\u00e1c th\u00e0nh qu\u1ea3 to\u00e1n h\u1ecdc m\u1edbi, \u0111\u00e3 th\u00fac \u0111\u1ea9y to\u00e1n h\u1ecdc ph\u00e1t tri\u1ec3n, \u0111i\u1ec1u \u0111\u00f3 khi\u1ebfn \u00fd ngh\u0129a c\u1ee7a \u0111\u1ecbnh l\u00ed Ferma v\u01b0\u1ee3t ra kh\u1ecfi khu\u00f4n kh\u1ed5 c\u1ee7a m\u1ed9t \u0111\u1ecbnh l\u00ed.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: \u0110\u1ecbnh l\u00ed l\u1edbn Ferma.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ch\u00fang ta \u0111\u1ec1u bi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh x2 + y2 = z2c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m kh\u00e1c kh\u00f4ng. V\u00ed d\u1ee5 b\u1ed9 ba s\u1ed1 g\u1ecdi l\u00e0 b\u1ed9 s\u1ed1 tam gi\u00e1c th\u1eddi Trung Qu\u1ed1c c\u1ed5 \u0111\u1ea1i c\u00f3 c\u1ea1nh g\u00f3c vu\u00f4ng l\u00e0 3, 4, \u0111\u01b0\u1eddng huy\u1ec1n l\u00e0 5 l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh x = 3; y = 4, z […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7670","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7670","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7670"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7670\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}