N\u0103m 1852, C\u00f4xuri t\u1ed1t nghi\u1ec7p \u0111\u1ea1i h\u1ecdc \u1edf Lu\u00e2n \u0110\u00f4n. Khi v\u1ebd \u0111\u1ecba \u0111\u1ed3, \u00f4ng nh\u1eadn th\u1ea5y: v\u1edbi m\u1ed9t t\u1ea5m b\u1ea3n \u0111\u1ed3 ch\u1ec9 c\u1ea7n d\u00f9ng t\u1ed1i \u0111a b\u1ed1n m\u00e0u l\u00e0 c\u00f3 th\u1ec3 t\u00f4 \u0111\u1ee7 \u0111\u1ec3 ph\u00e2n bi\u1ec7t \u0111\u01b0\u1ee3c c\u00e1c qu\u1ed1c gia c\u00f3 chung bi\u00ean gi\u1edbi, t\u1ee9c l\u00e0 m\u00e0u c\u1ee7a c\u00e1c qu\u1ed1c gia c\u00f3 chung bi\u00ean gi\u1edbi s\u1ebd kh\u00f4ng gi\u1ed1ng nhau.<\/p>\n\n\n\n
\u00d4ng li\u1ec1n \u0111\u1eb7t ra cho c\u00e1c anh em c\u1ee7a \u00f4ng \u0111ang c\u00f4ng t\u00e1c \u1edf tr\u01b0\u1eddng \u0111\u1ea1i h\u1ecdc l\u00e0 li\u1ec7u c\u00f3 th\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u0111i\u1ec1u \u0111\u00f3 kh\u00f4ng?<\/p>\n\n\n\n
C\u00e1c anh em c\u1ee7a \u00f4ng li\u1ec1n h\u1ecfi nh\u00e0 to\u00e1n h\u1ecdc M\u00f4can, M\u00f4can th\u1eeba nh\u1eadn l\u00e0 \u00f4ng ta kh\u00f4ng th\u1ec3 ph\u00e1n \u0111o\u00e1n \u0111\u01b0\u1ee3c \u0111\u00fang sai.<\/p>\n\n\n\n
Tho\u1ea1t nh\u00ecn, b\u00e0i to\u00e1n b\u1ed1n m\u00e0u kh\u00e1 \u0111\u01a1n gi\u1ea3n. B\u1ea1n ch\u1ec9 c\u1ea7n l\u1ea5y m\u1ed9t t\u1ea5m b\u1ea3n \u0111\u1ed3 ch\u01b0a t\u00f4 m\u00e0u v\u00e0 chu\u1ea9n b\u1ecb b\u1ed1n lo\u1ea1i m\u00e0u. Tr\u01b0\u1edbc h\u1ebft b\u1ea1n c\u00f3 th\u1ec3 t\u00f4 m\u1ed9t qu\u1ed1c gia n\u00e0o \u0111\u00f3 v\u00ed d\u1ee5 m\u00e0u \u0111\u1ecf, sau \u0111\u00f3 b\u1ea1n t\u00f4 c\u00e1c qu\u1ed1c gia l\u00e2n c\u1eadn b\u1eb1ng c\u00e1c m\u00e0u kh\u00e1c v\u00e0 theo \u201cnguy\u00ean t\u1eafc b\u1ed1n m\u00e0u\u201d b\u1ea1n s\u1ebd th\u1ea5y qu\u1ed1c gia c\u00f3 bi\u00ean gi\u1edbi chung s\u1ebd c\u00f3 m\u00e0u kh\u00e1c nhau, kh\u00f4ng gi\u1ed1ng nhau.<\/p>\n\n\n\n
Qu\u1ea3 l\u00e0 vi\u1ec7c \u0111\u00f3 s\u1ebd \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n kh\u00e1 d\u1ec5 d\u00e0ng. Tuy nhi\u00ean, \u0111\u00f3 ch\u1ec9 l\u00e0 s\u1ef1 ki\u1ec3m ch\u1ee9ng m\u00e0 kh\u00f4ng ph\u1ea3i l\u00e0 ch\u1ee9ng minh to\u00e1n h\u1ecdc. V\u1ea5n \u0111\u1ec1 b\u1ea3n \u0111\u1ed3 c\u00f3 b\u1ed1n m\u00e0u \u0111\u01b0\u1ee3c \u0111\u1eb7t ra nh\u01b0 m\u1ed9t b\u00e0i to\u00e1n l\u00e0 m\u1ed9t c\u00e1ch ph\u00e1n \u0111o\u00e1n chung m\u00e0 kh\u00f4ng h\u1ec1 ch\u1ec9 m\u1ed9t t\u1ea5m b\u1ea3n \u0111\u1ed3 c\u1ee5 th\u1ec3 n\u00e0o, l\u00e0 m\u1ed9t kh\u00e1i qu\u00e1t cho b\u1ea5t k\u00ec m\u1ed9t b\u1ea3n \u0111\u1ed3 n\u00e0o \u0111\u01b0\u1ee3c v\u1ebd tr\u00ean gi\u1ea5y. T\u1ea5m \u0111\u1ecba \u0111\u1ed3 \u1edf \u0111\u00e2y c\u00f3 th\u1ec3 l\u00e0 t\u1ea5m \u0111\u1ecba \u0111\u1ed3 th\u1ef1c m\u00e0 c\u0169ng c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t t\u1ea5m \u0111\u1ecba \u0111\u1ed3 t\u01b0\u1edfng t\u01b0\u1ee3ng, th\u1eadm ch\u00ed k\u1ec3 c\u1ea3 nh\u1eefng c\u00e1i m\u00e0 ng\u01b0\u1eddi ta ch\u01b0a h\u1ec1 ngh\u0129 \u0111\u00f3 l\u00e0 b\u1ea3n \u0111\u1ed3.<\/p>\n\n\n\n
C\u0169ng c\u00f3 ng\u01b0\u1eddi ngh\u0129 \u0111\u1ebfn c\u00e1c t\u1ea5m b\u1ea3n \u0111\u1ed3 m\u00e0 kh\u00f4ng \u0111\u1ee7 n\u0103m m\u00e0u th\u00ec kh\u00f4ng th\u1ec3 t\u00f4 \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n
Nh\u01b0 v\u1eady c\u00f3 th\u1ec3 th\u1ea5y b\u1ea3n \u0111\u1ed3 b\u1ed1n m\u00e0u t\u01b0\u1edfng nh\u01b0 \u0111\u01a1n gi\u1ea3n, m\u00e0 ch\u1ee9ng minh th\u00ec l\u1ea1i r\u1ea5t kh\u00f3. Sau n\u00e0y b\u00e0i to\u00e1n b\u1ea3n \u0111\u1ed3 b\u1ed1n m\u00e0u c\u00f9ng v\u1edbi \u0111\u1ecbnh l\u00ed l\u1edbn Fecma (Fermat) v\u00e0 b\u00e0i to\u00e1n G\u00f4n bach (Goldbach) \u0111\u01b0\u1ee3c xem l\u00e0 ba b\u00e0i to\u00e1n kh\u00f3 l\u1edbn c\u1ee7a th\u1eddi c\u1eadn \u0111\u1ea1i.<\/p>\n\n\n\n
N\u0103m 1879, Kenpu tuy\u00ean b\u1ed1 \u0111\u00e3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c b\u00e0i to\u00e1n b\u1ed1n m\u00e0u. M\u01b0\u1eddi m\u1ed9t n\u0103m sau, nh\u00e0 to\u00e1n h\u1ecdc Haut (Hawood) ch\u1ec9 ra r\u1eb1ng, c\u00e1ch ch\u1ee9ng minh c\u1ee7a Kenpu c\u00f3 ch\u1ed7 kh\u00f4ng ch\u1eb7t ch\u1ebd, n\u00ean c\u00e1ch ch\u1ee9ng minh \u0111\u01b0\u01a1ng nhi\u00ean kh\u00f4ng \u0111\u01b0\u1ee3c ch\u1ea5p nh\u1eadn. Haut \u0111\u00e3 \u1ee9ng d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p c\u1ee7a Kenpu v\u00e0 ch\u1ee9ng minh \u0111\u01b0\u1ee3c r\u1eb1ng, c\u1ea7n c\u00f3 n\u0103m m\u00e0u th\u00ec c\u00f3 th\u1ec3 t\u00f4 \u0111\u01b0\u1ee3c b\u1ea3n \u0111\u1ed3 th\u1ebf gi\u1edbi \u0111\u1ec3 cho c\u00e1c qu\u1ed1c gia c\u00f3 bi\u00ean gi\u1edbi chung kh\u00f4ng b\u1ecb tr\u00f9ng m\u00e0u. B\u00e0i to\u00e1n n\u00e0y c\u00f3 t\u00ean l\u00e0 \u201cb\u00e0i to\u00e1n n\u0103m m\u00e0u\u201d.<\/p>\n\n\n\n
T\u1eeb \u0111\u1ea7u th\u1ebf k\u1ec9 XX tr\u1edf l\u1ea1i \u0111\u00e2y, nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 \u0111i theo con \u0111\u01b0\u1eddng c\u1ee7a Kenpu \u0111\u1ec3 nghi\u00ean c\u1ee9u gi\u1ea3i b\u00e0i to\u00e1n b\u1ed1n m\u00e0u v\u00e0 \u0111\u00e3 thu \u0111\u01b0\u1ee3c nhi\u1ec1u th\u00e0nh t\u1ef1u. Ng\u01b0\u1eddi ta ch\u1ee9ng minh l\u00e0 \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n n\u00e0y ta kh\u00f4ng ch\u1ec9 ngh\u0129 \u0111\u1ebfn m\u1ed9t t\u1ea5m b\u1ea3n \u0111\u1ed3 \u0111\u00e3 v\u1ebd s\u1eb5n m\u00e0 ph\u1ea3i ngh\u0129 \u0111\u1ec3 v\u1ebd ra v\u00f4 s\u1ed1 t\u1ea5m b\u1ea3n \u0111\u1ed3. \u0110\u1ec3 ki\u1ec3m nghi\u1ec7m s\u1ed1 l\u1edbn b\u1ea3n \u0111\u1ed3 nh\u01b0 v\u1eady qu\u1ea3 l\u00e0 m\u1ed9t vi\u1ec7c c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng l\u1edbn qu\u00e1 s\u1ee9c ng\u01b0\u1eddi v\u00e0 kh\u00f3 th\u1ef1c hi\u1ec7n \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n
V\u00e0o n\u0103m 1970 \u0111\u00e3 c\u00f3 ph\u01b0\u01a1ng \u00e1n d\u00f9ng m\u00e1y t\u00ednh \u0111i\u1ec7n t\u1eed \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n n\u00e0y, v\u00e0 ng\u01b0\u1eddi ta \u0111\u00e3 ph\u1ea3i t\u00ednh to\u00e1n 11 n\u0103m li\u00ean t\u1ee5c m\u1edbi t\u00ecm \u0111\u01b0\u1ee3c k\u1ebft lu\u1eadn.<\/p>\n\n\n\n
Sau n\u0103m 1970, nhi\u1ec1u ng\u01b0\u1eddi \u0111\u00e3 c\u1ea3i ti\u1ebfn ph\u01b0\u01a1ng \u00e1n gi\u1ea3i b\u00e0i to\u00e1n b\u1ed1n m\u00e0u k\u1ebft h\u1ee3p v\u1edbi s\u1ef1 t\u0103ng nhanh t\u1ed1c \u0111\u1ed9 t\u00ednh c\u1ee7a m\u00e1y \u0111i\u1ec7n to\u00e1n \u0111\u00e3 m\u1edf ra kh\u1ea3 n\u0103ng gi\u1ea3i \u0111\u01b0\u1ee3c b\u00e0i to\u00e1n b\u1ed1n m\u00e0u b\u1eb1ng m\u00e1y t\u00ednh.<\/p>\n\n\n\n
V\u00e0o n\u0103m 1976, hai nh\u00e0 to\u00e1n h\u1ecdc Hoa K\u00ec l\u00e0 Apin (Apeil) v\u00e0 Hakan (Hakan) \u0111\u00e3 d\u00f9ng ba m\u00e1y \u0111i\u1ec7n to\u00e1n kh\u00e1c nhau v\u00e0 \u0111\u00e3 d\u00f9ng \u0111\u1ebfn 1200 gi\u1edd \u0111\u1ec3 ho\u00e0n ch\u1ec9nh vi\u1ec7c ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed v\u1ec1 b\u00e0i to\u00e1n b\u1ed1n m\u00e0u.<\/p>\n\n\n\n
B\u00e0i to\u00e1n b\u1ed1n m\u00e0u t\u1eeb khi \u0111\u1eb7t ra cho \u0111\u1ebfn khi ph\u00e1t tri\u1ec3n th\u00e0nh \u0111\u1ecbnh l\u00ed \u0111\u00e3 tr\u1ea3i qua 120 n\u0103m l\u00e0m vi\u1ec7c li\u00ean t\u1ee5c c\u1ee7a nhi\u1ec1u th\u1ebf h\u1ec7 c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc m\u1edbi \u0111\u01b0\u1ee3c ho\u00e0n th\u00e0nh. Cho \u0111\u1ebfn ng\u00e0y nay, nhi\u1ec1u nh\u00e0 khoa h\u1ecdc v\u1eabn \u0111ang t\u00ecm ki\u1ebfm l\u1eddi gi\u1ea3i b\u1eb1ng t\u00ednh to\u00e1n tr\u00ean m\u1eb7t gi\u1ea5y.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: B\u1ea3n \u0111\u1ed3 b\u1ed1n m\u00e0u; B\u00e0i to\u00e1n b\u1ed1n m\u00e0u; \u0110\u1ecbnh l\u00ed b\u1ed1n m\u00e0u.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
N\u0103m 1852, C\u00f4xuri t\u1ed1t nghi\u1ec7p \u0111\u1ea1i h\u1ecdc \u1edf Lu\u00e2n \u0110\u00f4n. Khi v\u1ebd \u0111\u1ecba \u0111\u1ed3, \u00f4ng nh\u1eadn th\u1ea5y: v\u1edbi m\u1ed9t t\u1ea5m b\u1ea3n \u0111\u1ed3 ch\u1ec9 c\u1ea7n d\u00f9ng t\u1ed1i \u0111a b\u1ed1n m\u00e0u l\u00e0 c\u00f3 th\u1ec3 t\u00f4 \u0111\u1ee7 \u0111\u1ec3 ph\u00e2n bi\u1ec7t \u0111\u01b0\u1ee3c c\u00e1c qu\u1ed1c gia c\u00f3 chung bi\u00ean gi\u1edbi, t\u1ee9c l\u00e0 m\u00e0u c\u1ee7a c\u00e1c qu\u1ed1c gia c\u00f3 chung bi\u00ean […]<\/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-7672","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\/7672","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=7672"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7672\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7672"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7672"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7672"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}