V\u00e0o ng\u00e0y 7-6-1742, nh\u00e0 to\u00e1n h\u1ecdc \u0110\u1ee9c Goldbach \u0111\u00e3 g\u1eedi cho gi\u00e1o s\u01b0 Euler m\u1ed9t d\u1ef1 \u0111o\u00e1n \u201cB\u1ea5t k\u00ec m\u1ed9t s\u1ed1 l\u1ebb n\u00e0o l\u1edbn h\u01a1n 5 \u0111\u1ec1u l\u00e0 t\u1ed5ng c\u1ee7a 3 s\u1ed1 nguy\u00ean t\u1ed1\u201d. Ng\u00e0y 30-6 n\u0103m \u0111\u00f3, Euler \u0111\u00e3 vi\u1ebft th\u01b0 tr\u1ea3 l\u1eddi Goldbach cho r\u1eb1ng d\u1ef1 \u0111o\u00e1n l\u00e0 ch\u00ednh x\u00e1c v\u00e0 \u0111\u01b0a ra m\u1ed9t d\u1ef1 \u0111o\u00e1n \u201cB\u1ea5t k\u00ec m\u1ed9t s\u1ed1 ch\u1eb5n n\u00e0o l\u1edbn h\u01a1n hai \u0111\u1ec1u l\u00e0 t\u1ed5ng c\u1ee7a hai s\u1ed1 nguy\u00ean t\u1ed1”, nh\u01b0ng b\u1ea5y gi\u1edd h\u1ecd \u0111\u00e3 kh\u00f4ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c c\u00e1c m\u1ec7nh \u0111\u1ec1 \u0111\u00f3.<\/p>\n\n\n\n
Hai v\u1ea5n \u0111\u1ec1 n\u00e0y \u0111\u00e3 l\u00f4i cu\u1ed1n s\u1ef1 h\u1ee9ng th\u00fa c\u1ee7a \u0111\u00f4ng \u0111\u1ea3o c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc, \u0111\u00f3 ch\u00ednh l\u00e0 \u201cd\u1ef1 \u0111o\u00e1n Goldbach\u201d n\u1ed5i ti\u1ebfng. T\u1eeb \u0111\u00f3 \u0111\u00e3 b\u1eaft \u0111\u1ea7u m\u1ed9t c\u00f4ng cu\u1ed9c ch\u1ee9ng minh gian nan \u201cd\u1ef1 \u0111o\u00e1n Goldbach\u201d.<\/p>\n\n\n\n
Do d\u1ef1 \u0111o\u00e1n Goldbach m\u1ed9t th\u1eddi gian d\u00e0i ch\u01b0a \u0111\u01b0\u1ee3c ch\u1ee9ng minh n\u00ean t\u1ea1i H\u1ed9i ngh\u1ecb qu\u1ed1c t\u1ebf to\u00e1n h\u1ecdc n\u0103m 1912 \u0111\u01b0a ra m\u1ed9t d\u1ef1 \u0111o\u00e1n y\u1ebfu \u1edbt h\u01a1n: T\u1ed3n t\u1ea1i m\u1ed9t s\u1ed1 nguy\u00ean C \u0111\u1ec3 cho m\u1ed9t s\u1ed1 nguy\u00ean l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 2 s\u1ebd \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng t\u1ed5ng hai s\u1ed1 nguy\u00ean t\u1ed1 kh\u00f4ng l\u1edbn h\u01a1n C.<\/p>\n\n\n\n
N\u0103m 1930, nh\u00e0 to\u00e1n h\u1ecdc Li\u00ean X\u00f4 25 tu\u1ed5i l\u00e0 Sineyrilman \u0111\u00e3 \u0111\u01b0a ra ch\u1ee9ng minh cho m\u1ec7nh \u0111\u1ec1 C. \u00d4ng c\u00f2n \u0111\u01b0a ra m\u1ec7nh \u0111\u1ec1 v\u1edbi \u0111i\u1ec1u ki\u1ec7n C kh\u00f4ng l\u1edbn h\u01a1n S, S \u2264 800.000. Sau n\u00e0y S \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 s\u1ed1 Sineyrilman. \u0110\u00e2y l\u00e0 b\u01b0\u1edbc \u0111\u1ed9t ph\u00e1 trong qu\u00e1 tr\u00ecnh ch\u1ee9ng minh d\u1ef1 \u0111o\u00e1n Goldbach.<\/p>\n\n\n\n
N\u0103m 1937, nh\u00e0 to\u00e1n h\u1ecdc Li\u00ean X\u00f4 Vinogradov \u0111\u00e3 d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p \u201cvi\u00ean chu\u201d v\u00e0 ph\u01b0\u01a1ng ph\u00e1p do \u00f4ng s\u00e1ng t\u1ea1o l\u00e0 ph\u01b0\u01a1ng ph\u00e1p ph\u1ed1i h\u1ee3p \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng: V\u1edbi m\u1ed9t s\u1ed1 l\u1ebb \u0111\u1ee7 l\u1edbn \u0111\u1ec1u c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n b\u1eb1ng t\u1ed5ng c\u1ee7a ba s\u1ed1 nguy\u00ean t\u1ed1 l\u1ebb.<\/p>\n\n\n\n
\u0110\u00e2y l\u1ea1i l\u00e0 b\u01b0\u1edbc \u0111\u1ed9t ph\u00e1 l\u1edbn nh\u1ea5t \u0111\u1ec3 gi\u1ea3i quy\u1ebft d\u1ef1 \u0111o\u00e1n Goldbach v\u00e0 \u0111\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ecbnh l\u00ed ba s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n\n\n
Trong qu\u00e1 tr\u00ecnh ch\u1ee9ng minh d\u1ef1 \u0111o\u00e1n Goldbach ng\u01b0\u1eddi \u0111\u00e3 \u0111\u01b0a ra m\u1ec7nh \u0111\u1ec1, v\u1edbi m\u1ed9t s\u1ed1 ch\u1eb5n \u0111\u1ee7 l\u1edbn, ta c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n b\u1eb1ng c\u00e1c nh\u00e2n t\u1eed v\u00e0 kh\u00f4ng v\u01b0\u1ee3t qu\u00e1 t\u1ed5ng c\u00e1c nh\u00e2n t\u1eed l\u00e0 m v\u00e0 n nh\u00e2n v\u1edbi hai s\u1ed1 n\u00e0o \u0111\u00f3.<\/p>\n\n\n\n
M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u01b0\u1ee3c ghi l\u00e0 \u201c m + n\u201d. V\u00ed d\u1ee5 \u201c3 + 4\u201d l\u00e0 ph\u1ea3i ch\u1ee9ng minh v\u1edbi s\u1ed1 ch\u1eb5n \u0111\u1ee7 l\u1edbn th\u00ec c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n b\u1eb1ng t\u1ed5ng c\u00e1c nh\u00e2n t\u1eed l\u00e0 3, nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 v\u00e0 4 nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 kh\u00e1c. C\u00f2n \u201c1 + 1\u201d c\u00f3 ngh\u0129a v\u1edbi s\u1ed1 ch\u1eb5n \u0111\u1ee7 l\u1edbn th\u00ec c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n b\u1eb1ng t\u1ed5ng hai s\u1ed1 nguy\u00ean t\u1ed1. N\u1ebfu ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u201c1 + 1\u201d th\u00ec tr\u00ean c\u01a1 b\u1ea3n l\u00e0 ch\u1ee9ng minh \u0111\u01b0\u1ee3c d\u1ef1 \u0111o\u00e1n Goldbach \u201c\u0110\u1ecbnh l\u00ed ba s\u1ed1 nguy\u00ean t\u1ed1\u201d ch\u1ec9 l\u00e0 lo\u1ea1i suy \u0111o\u00e1n quan tr\u1ecdng t\u1eeb d\u1ef1 \u0111o\u00e1n Goldbach.<\/p>\n\n\n\n
N\u0103m 1920, nh\u00e0 to\u00e1n h\u1ecdc Na Uy \u0111\u00e3 c\u1ea3i ti\u1ebfn \u201cph\u01b0\u01a1ng ph\u00e1p r\u00e2y\u201d ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u201c 9 + 9\u201d. N\u0103m 1924, nh\u00e0 to\u00e1n h\u1ecdc \u0110\u1ee9c Radama ch\u1ee9ng minh \u201c 7 + 7\u201d. N\u0103m 1932, nh\u00e0 to\u00e1n h\u1ecdc Anh Eistman \u0111\u00e3 ch\u1ee9ng minh \u201c6 + 6\u201d. V\u1ec1 sau, n\u0103m 1938 v\u00e0 n\u0103m 1940, Buhaxitabov \u0111\u00e3 ch\u1ee9ng minh \u201c5 + 5\u201d v\u00e0 \u201c4 + 4\u201d. V\u00e0o n\u0103m 1956, nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c V\u01b0\u01a1ng Nguy\u00ean \u0111\u00e3 ch\u1ee9ng minh \u201c3 + 4\u201d, nh\u00e0 to\u00e1n h\u1ecdc Li\u00ean X\u00f4 Vinogradov ch\u1ee9ng minh \u201c3 + 3\u201d. N\u0103m 1957, V\u01b0\u01a1ng Nguy\u00ean ch\u1ee9ng minh \u201c2 + 3\u201d.<\/p>\n\n\n\n
Vi\u1ec7c ch\u1ee9ng minh c\u00f3 \u201c1\u201d \u0111\u1ea7u ti\u00ean ra \u0111\u1eddi s\u1edbm nh\u1ea5t v\u00e0o n\u0103m 1848 do nh\u00e0 to\u00e1n h\u1ecdc Hungari Reny th\u1ef1c hi\u1ec7n. Reny \u0111\u00e3 ch\u1ee9ng minh \u201c1 + c\u201d, trong \u0111\u00f3 c l\u00e0 h\u1eb1ng s\u1ed1 r\u1ea5t l\u1edbn. N\u0103m 1962, nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c Phan Th\u1eeba \u0110\u1ed9ng ch\u1ee9ng minh \u201c1 + 5\u201d. C\u00f9ng n\u0103m \u0111\u00f3 nh\u00e0 to\u00e1n h\u1ecdc Li\u00ean<\/p>\n\n\n\n
X\u00f4 Barbaen c\u0169ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u201c1 + 5\u201d. V\u00e0o n\u0103m 1963, V\u01b0\u01a1ng Nguy\u00ean v\u00e0 Phan Th\u1eeba \u0110\u1ed9ng, Barbaen c\u00f9ng l\u00fac ch\u1ee9ng minh \u201c1 + 4\u201d. N\u0103m 1965, Vinogradov v\u00e0 Buagaxitabov v\u00e0 nh\u00e0 to\u00e1n h\u1ecdc Italia Benpini ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u201c1 + 3\u201d.<\/p>\n\n\n\n
N\u0103m 1966, nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c Tr\u1ea7n C\u1ea3nh Nhu\u1eadn l\u1ea1i m\u1ed9t l\u1ea7n n\u1eefa c\u1ea3i ti\u1ebfn \u201cph\u01b0\u01a1ng ph\u00e1p r\u00e2y\u201d v\u00e0 \u0111\u00e3 ch\u1ee9ng minh \u201c1 + 2\u201d, nh\u01b0ng ch\u01b0a ph\u00e1t bi\u1ec3u r\u00f5 r\u00e0ng c\u00e1c ch\u1ee9ng minh c\u1ee7a m\u00ecnh n\u00ean kh\u00f4ng c\u00f3 ti\u1ebfng vang l\u1edbn tr\u00ean th\u1ebf gi\u1edbi. V\u00e0o n\u0103m 1973, Tr\u1ea7n C\u1ea3nh Nhu\u1eadn l\u1ea1i s\u1eeda ch\u1eefa l\u1ea1i lu\u1eadn v\u0103n c\u1ee7a m\u00ecnh v\u00e0 ph\u00e1t bi\u1ec3u \u201cm\u1ed9t s\u1ed1 ch\u1eb5n l\u1edbn \u0111\u1ec1u c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n b\u1eb1ng t\u1ed5ng hai s\u1ed1 trong \u0111\u00f3 c\u00f3 m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1 c\u00f2n s\u1ed1 kia ho\u1eb7c l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1 ho\u1eb7c l\u00e0 t\u00edch hai s\u1ed1 nguy\u00ean t\u1ed1\u201d. Ch\u1ee9ng minh c\u1ee7a Tr\u1ea7n C\u1ea3nh Nhu\u1eadn \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ecbnh l\u00ed h\u1ecd Tr\u1ea7n. Lu\u1eadn v\u0103n c\u1ee7a Tr\u1ea7n C\u1ea3nh Nhu\u1eadn \u0111\u01b0\u1ee3c gi\u1edbi to\u00e1n h\u1ecdc h\u01b0\u1edfng \u1ee9ng nhi\u1ec7t li\u1ec7t. Kh\u00f4ng \u00edt nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 c\u1ed1 g\u1eafng ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n h\u01a1n. C\u00e1c ch\u1ee9ng minh \u0111\u01a1n gi\u1ea3n l\u00e0 c\u1ee7a c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc V\u01b0\u01a1ng Nguy\u00ean, \u0110\u1ecbnh H\u1ea1 Hu\u1ec1, Phan Th\u1eeba \u0110\u1ed9ng, c\u00f9ng c\u00e1c c\u1ed9ng t\u00e1c vi\u00ean ti\u1ebfn h\u00e0nh.<\/p>\n\n\n\n
D\u1ef1 \u0111o\u00e1n Goldbach l\u00e0 d\u1ef1 \u0111o\u00e1n quan tr\u1ecdng c\u1ee7a l\u00ed thuy\u1ebft v\u1ec1 s\u1ed1 \u0111\u01b0\u1ee3c \u0111\u01b0a ra c\u00e1ch \u0111\u00e2y \u0111\u00e3 h\u01a1n 250 n\u0103m, nh\u01b0ng v\u1eabn c\u00f2n ch\u01b0a ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u0111\u1ebfn c\u00f9ng v\u00e0 ch\u01b0a th\u00e0nh \u0111\u1ecbnh l\u00ed. Qua g\u1ea7n 70 n\u0103m n\u1ed7 l\u1ef1c, c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc tr\u00ean to\u00e0n th\u1ebf gi\u1edbi \u0111\u00e3 thu \u0111\u01b0\u1ee3c nh\u1eefng b\u01b0\u1edbc ti\u1ebfn r\u1ea5t l\u1edbn v\u00e0 hi\u1ec7n nay ng\u01b0\u1eddi ta \u0111ang ti\u1ebfn qu\u00e2n v\u00e0o \u201c1 + 1\u201d.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: S\u1ed1 nguy\u00ean t\u1ed1; D\u1ef1 \u0111o\u00e1n Goldbach; \u0110\u1ecbnh l\u00ed ba nguy\u00ean<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
V\u00e0o ng\u00e0y 7-6-1742, nh\u00e0 to\u00e1n h\u1ecdc \u0110\u1ee9c Goldbach \u0111\u00e3 g\u1eedi cho gi\u00e1o s\u01b0 Euler m\u1ed9t d\u1ef1 \u0111o\u00e1n \u201cB\u1ea5t k\u00ec m\u1ed9t s\u1ed1 l\u1ebb n\u00e0o l\u1edbn h\u01a1n 5 \u0111\u1ec1u l\u00e0 t\u1ed5ng c\u1ee7a 3 s\u1ed1 nguy\u00ean t\u1ed1\u201d. Ng\u00e0y 30-6 n\u0103m \u0111\u00f3, Euler \u0111\u00e3 vi\u1ebft th\u01b0 tr\u1ea3 l\u1eddi Goldbach cho r\u1eb1ng d\u1ef1 \u0111o\u00e1n l\u00e0 ch\u00ednh x\u00e1c v\u00e0 \u0111\u01b0a ra […]<\/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-7668","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\/7668","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=7668"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7668\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}