Ta h\u00e3y x\u00e9t xem hai t\u1ed5ng m\u1ed7i t\u1ed5ng l\u00e0 s\u00e1u s\u1ed1 t\u1ef1 nhi\u00ean: 1 + 6 + 7 + 17 + 18 + 23 = 2 + 3 + 11 + 13 + 21 + 22<\/p>\n\n\n\n
B\u1ea1n s\u1ebd th\u1ed1t l\u00ean th\u1ebf th\u00ec c\u00f3 g\u00ec l\u00e0 l\u1ea1 12 + 62 + 72 + 172 + 182 + 232 = 22 + 32 + 112 + 132+ 212 + 222<\/p>\n\n\n\n
B\u00e2y gi\u1edd ch\u1eafc b\u1ea1n s\u1ebd c\u1ea3m th\u1ea5y c\u00f3 \u0111i\u1ec1u kh\u00e1c th\u01b0\u1eddng. Qu\u1ea3 l\u00e0 b\u1ea1n s\u1ebd th\u1ea5y h\u1ebft s\u1ee9c th\u00fa v\u1ecb khi ta ti\u1ebfp t\u1ee5c: 13 + 63 + 73 + 173 + 183 + 233 = 23 + 33 + 113 + 133 + 213 + 223 14 + 64 + 74 + 174 + 184 + 234 = 24 + 34 + 114 + 134 + 214 + 224 15 + 65 + 75+ 175 +185 +235 = 25 + 35 + 115+ 135 + 215 + 225<\/p>\n\n\n\n
Th\u1ebf nh\u01b0ng li\u1ec7u c\u00f3 \u0111i\u1ec3m d\u1eebng hay kh\u00f4ng? C\u00e1c \u0111\u1eb3ng th\u1ee9c b\u1eadc 6 b\u1eadc 7 v.v\u2026 d\u00f9 c\u00f3 th\u1ef1c hi\u1ec7n kh\u00f3 kh\u0103n b\u1ea1n c\u0169ng c\u00f3 th\u1ec3 t\u00ecm \u0111\u01b0\u1ee3c v\u00e0 t\u1ea5m m\u00e0n \u0111\u1eb3ng th\u1ee9c ch\u1ec9 d\u1eebng l\u1ea1i \u1edf lu\u1ef9 th\u1eeba b\u1eadc 9.<\/p>\n\n\n\n
Hai nh\u00f3m s\u1ed1 n\u00e0y do Fuyi ngh\u0129 ra. Qu\u1ea3 l\u00e0 k\u00ec di\u1ec7u. Th\u1ebf nh\u01b0ng c\u01a1 s\u1edf c\u1ee7a ch\u00fang l\u00e0 g\u00ec, d\u1ef1a v\u00e0o \u0111\u00e2u ng\u01b0\u1eddi ta ngh\u0129 ra. Ngo\u00e0i hai nh\u00f3m s\u1ed1 n\u00e0y c\u00f2n con s\u1ed1 n\u00e0o kh\u00e1c kh\u00f4ng?<\/p>\n\n\n\n
Nh\u00e0 to\u00e1n h\u1ecdc n\u1ed5i ti\u1ebfng Li\u00ean X\u00f4 tr\u01b0\u1edbc \u0111\u00e2y- Gelfan \u0111\u00e3 gi\u1ea3i \u0111\u00e1p c\u00e2u h\u1ecfi n\u00e0y. Nguy\u00ean do c\u00e1c nh\u00f3m s\u1ed1 n\u00e0y xu\u1ea5t ph\u00e1t t\u1eeb c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c sau \u0111\u00e2y: an + a(a + 4b + c)n + (a + b + 2c)n + (a + 9b + 4c)n + (a + 6b + 5c)n + (a + 10b + 6c)n = = (a + b)n + (a + c)n + (a + 6b + 2c)n + (a + 4b + 4c)n + (a + 10b + 5c)n + (a + 9b + 6c)n<\/p>\n\n\n\n
Trong \u0111\u00f3 n = 1,2,3,4,5. C\u00e1c nh\u00f3m s\u1ed1 v\u1eeba n\u00eau tr\u00ean t\u1ea1o th\u00e0nh t\u1eeb a = 1, b = 1, v\u00e0 c = 2. N\u1ebfu ch\u1ecdn a, b, c l\u00e0 c\u00e1c s\u1ed1 kh\u00e1c ng\u01b0\u1eddi ta s\u1ebd nh\u1eadn \u0111\u01b0\u1ee3c c\u00e1c nh\u00f3m s\u1ed1 kh\u00e1c c\u00f3 t\u00ednh ch\u1ea5t t\u01b0\u01a1ng t\u1ef1 v\u00e0 kh\u00f4ng k\u1ec3 h\u1ebft \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n
V\u1ea5n \u0111\u1ec1 t\u01b0\u01a1ng t\u1ef1 g\u1ecdi l\u00e0 \u201cv\u1ea5n \u0111\u1ec1 b\u1ee9c m\u00e0n \u0111\u1eb3ng th\u1ee9c c\u00e1c t\u1ed5ng s\u1ed1 lu\u1ef9 th\u1eeba k\u201d, g\u1ecdi v\u1eafn t\u1eaft l\u00e0 \u201cv\u1ea5n \u0111\u1ec1 b\u1ee9c m\u00e0n \u0111\u1eb3ng th\u1ee9c c\u00e1c t\u1ed5ng s\u1ed1\u201d.<\/p>\n\n\n\n
Nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c qu\u00e1 c\u1ed1 Hoa La Canh \u0111\u00e3 t\u1eebng nghi\u00ean c\u1ee9u v\u00e0 \u0111\u00e3 \u0111\u1ea1t \u0111\u01b0\u1ee3c nhi\u1ec1u th\u00e0nh qu\u1ea3. Hi\u1ec7n t\u1ea1i ng\u01b0\u1eddi ta \u0111\u00e3 t\u00ednh \u0111\u1ebfn c\u00e1c lu\u1ef9 th\u1eeba b\u1eadc 9, b\u1eadc 10, th\u1ebf nh\u01b0ng v\u1ea5n \u0111\u1ec1 c\u00f2n ch\u01b0a \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft \u0111\u1ebfn c\u00f9ng. Lu\u1ef9 th\u1eeba b\u1eadc cao nh\u1ea5t v\u1eabn ch\u01b0a t\u00ecm th\u1ea5y. Li\u1ec7u k c\u00f3 gi\u1edbi h\u1ea1n tr\u00ean kh\u00f4ng? V\u01b0\u1ee3t qua gi\u1edbi h\u1ea1n \u0111\u00f3 li\u1ec7u c\u00f3 th\u1ec3 \u0111\u1eb3ng th\u1ee9c c\u00f2n \u0111\u00fang kh\u00f4ng?<\/p>\n\n\n\n
T\u1eeb kho\u00e1: B\u1ee9c m\u00e0n \u0111\u1eb3ng th\u1ee9c l\u0169y th\u1eeba k.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ta h\u00e3y x\u00e9t xem hai t\u1ed5ng m\u1ed7i t\u1ed5ng l\u00e0 s\u00e1u s\u1ed1 t\u1ef1 nhi\u00ean: 1 + 6 + 7 + 17 + 18 + 23 = 2 + 3 + 11 + 13 + 21 + 22 B\u1ea1n s\u1ebd th\u1ed1t l\u00ean th\u1ebf th\u00ec c\u00f3 g\u00ec l\u00e0 l\u1ea1 12 + 62 + 72 + 172 + 182 […]<\/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-7525","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\/7525","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=7525"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7525\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7525"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7525"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7525"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}