Ch\u00fang ta \u0111\u00e3 bi\u1ebft \u0111\u1ebfn \u0111\u1ecbnh l\u00ed th\u1eb7ng d\u01b0 Trung Qu\u1ed1c, t\u1ee9c v\u1ea5n \u0111\u1ec1 H\u00e0n T\u00edn \u0111i\u1ec3m binh, \u0111\u00f3 l\u00e0 m\u1ed9t th\u00e0nh t\u1ef1u quan tr\u1ecdng trong to\u00e1n h\u1ecdc Trung Qu\u1ed1c c\u1ed5 \u0111\u1ea1i, v\u1edbi n\u1ed9i dung thu\u1ed9c v\u1ec1 gi\u1ea3i ph\u00e1p d\u00e3y \u0111\u1ed3ng d\u01b0 m\u1ed9t l\u1ea7n trong l\u00ed thuy\u1ebft s\u1ed1. Hi\u1ec7n nay, ng\u01b0\u1eddi ta \u0111\u00e3 t\u00ecm ra c\u00f4ng d\u1ee5ng m\u1edbi c\u1ee7a th\u1ee9 ki\u1ebfn th\u1ee9c c\u1ed5 x\u01b0a n\u00e0y trong vi\u1ec7c m\u00e3 h\u00f3a m\u00e1y t\u00ednh.<\/p>\n\n\n\n
\u0110\u00e1p \u00e1n cho b\u00e0i to\u00e1n H\u00e0n T\u00edn \u0111i\u1ec3m binh c\u00f3 th\u1ec3 l\u00e0 r\u1ea5t nhi\u1ec1u, gi\u1eefa ch\u00fang l\u1ea1i c\u00f3 t\u01b0\u01a1ng sai l\u00e0 105 (t\u1ee9c 3 x 5x 7), song \u0111\u00e1p \u00e1n trong v\u00f2ng 105 th\u00ec l\u1ea1i ch\u1ec9 c\u00f3 m\u1ed9t. B\u00e2y gi\u1edd ch\u00fang ta h\u00e3y gi\u1ea3n h\u00f3a ch\u00fang: nh\u1eefng s\u1ed1 nguy\u00ean n\u00e0o c\u00f3 th\u1ec3 chia 3 th\u00ec d\u01b0 2, chia 5 th\u00ec d\u01b0 3? Kh\u00f4ng kh\u00f3 \u0111\u1ec3 t\u00ecm ra l\u00e0 8, 23, 38, 53,\u2026, gi\u1eefa ch\u00fang c\u00f3 t\u01b0\u01a1ng sai 15 (t\u1ee9c 3 x 5). C\u00f2n \u0111\u00e1p \u00e1n cho trong v\u00f2ng 15 ch\u1ec9 c\u00f3 m\u1ed9t: 8. V\u1eady th\u00ec, v\u1edbi \u0111\u1ec1 b\u00e0i nh\u01b0 v\u1eady c\u00f3 th\u1ec3 c\u00f3 bao nhi\u00eau b\u00e0i to\u00e1n? B\u00e0i to\u00e1n chia 3, s\u1ed1 d\u01b0 c\u00f3 th\u1ec3 l\u00e0 0, 1, 2, t\u1ed5ng c\u1ed9ng 3 lo\u1ea1i; B\u00e0i to\u00e1n chia 5, s\u1ed1 d\u01b0 c\u00f3 th\u1ec3 l\u00e0 0, 1, 2, 3, 4, t\u1ed5ng c\u1ed9ng 5 lo\u1ea1i, h\u1ee3p l\u1ea1i t\u1ed5ng c\u1ed9ng 3 x 5, t\u1ee9c 15 lo\u1ea1i. Ngh\u0129a l\u00e0 c\u00f3 th\u1ec3 c\u00f3 15 \u0111\u1ec1 b\u00e0i nh\u01b0 v\u1eady, \u0111\u00e1p \u00e1n kh\u00f4ng gi\u1ed1ng nhau, h\u01a1n n\u1eefa \u0111\u00e1p \u00e1n trong v\u00f2ng 15 th\u00ec l\u1ea1i ch\u1ec9 c\u00f3 m\u1ed9t. C\u00f3 th\u1ec3 th\u1ea5y, \u0111\u00e1p \u00e1n cho 15 \u0111\u1ec1 b\u00e0i n\u00e0y v\u1eeba v\u1eb7n t\u01b0\u01a1ng \u1ee9ng v\u1edbi 1, 2, 3,\u2026, 15.<\/p>\n\n\n\n
B\u00e2y gi\u1edd, \u0111i\u1ec1n 15 s\u1ed1 n\u00e0y v\u00e0o h\u00ecnh vu\u00f4ng 3 h\u00e0ng 5 c\u1ed9t (3 x 5), sao cho h\u00e0ng ngang l\u00e0 c\u00e1c s\u1ed1 chia cho 3 c\u00f3 d\u01b0; h\u00e0ng d\u1ecdc l\u00e0 c\u00e1c s\u1ed1 chia cho 5 c\u00f3 d\u01b0. V\u00ed d\u1ee5 8 l\u00e0 s\u1ed1 chia cho 3 d\u01b0 2, th\u00ec \u0111i\u1ec1n v\u00e0o h\u00e0ng th\u1ee9 hai, n\u00f3 l\u1ea1i l\u00e0 s\u1ed1 chia 5 d\u01b0 3, th\u00ec \u0111i\u1ec1n v\u00e0o c\u1ed9t th\u1ee9 ba.<\/p>\n\n\n\n
B\u1ea5t c\u1ee9 m\u1ed9t m\u00e1y t\u00ednh n\u00e0o c\u0169ng \u0111\u1ec1u c\u00f3 m\u1ed9t \u0111\u1ed9 d\u00e0i t\u1eeb (word length) nh\u1ea5t \u0111\u1ecbnh. \u0110\u1ed9 d\u00e0i t\u1eeb ch\u00ednh l\u00e0 con s\u1ed1 (digit) l\u1edbn nh\u1ea5t m\u00e0 m\u00e1y t\u00ednh c\u00f3 th\u1ec3 x\u1eed l\u00ed \u0111\u01b0\u1ee3c. V\u1eady th\u00ec, khi ch\u00fang ta c\u1ea7n s\u1eed d\u1ee5ng m\u00e1y t\u00ednh \u0111\u1ec3 x\u1eed l\u00ed m\u1ed9t d\u1eef li\u1ec7u c\u00f3 c\u00e1c s\u1ed1 v\u01b0\u1ee3t qu\u00e1 \u0111\u1ed9 d\u00e0i t\u1eeb \u0111\u00e3 \u0111\u1ecbnh th\u00ec l\u00e0m th\u1ebf n\u00e0o?<\/p>\n\n\n\n
Bi\u1ec7n ph\u00e1p th\u00f4ng th\u01b0\u1eddng l\u00e0 bi\u1ec3u th\u1ecb s\u1ed1 l\u1edbn \u1ea5y b\u1eb1ng hai s\u1ed1 nh\u1ecf h\u01a1n. Bi\u1ec7n ph\u00e1p \u0111\u01a1n gi\u1ea3n nh\u1ea5t l\u00e0 chia s\u1ed1 l\u1edbn th\u00e0nh hai \u0111o\u1ea1n, nh\u01b0 c\u00f3 th\u1ec3 chia 3517 th\u00e0nh hai s\u1ed1 nh\u1ecf h\u01a1n l\u00e0 35 v\u00e0 17. Nh\u01b0ng l\u00e0m nh\u01b0 v\u1eady th\u00ec m\u00e1y t\u00ednh khi thao t\u00e1c s\u1ebd kh\u00f3 h\u01a1n, cho n\u00ean ng\u01b0\u1eddi ta th\u01b0\u1eddng cho l\u00e0 kh\u00f4ng n\u00ean \u00e1p d\u1ee5ng.<\/p>\n\n\n\n
S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed th\u1eb7ng d\u01b0 c\u1ee7a Trung Qu\u1ed1c c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb (ho\u1eb7c m\u00e3 h\u00f3a) m\u1ed9t s\u1ed1 l\u1edbn b\u1eb1ng hai s\u1ed1 nh\u1ecf h\u01a1n, \u0111\u1ed3ng th\u1eddi l\u1ea1i khi\u1ebfn cho m\u00e1y t\u00ednh thao t\u00e1c h\u1ebft s\u1ee9c thu\u1eadn ti\u1ec7n. Ch\u00fang ta h\u00e3y nh\u00ecn l\u1ea1i h\u00ecnh vu\u00f4ng 3×5 \u1edf tr\u00ean, 8 \u0111\u01b0\u1ee3c s\u1eafp v\u00e0 h\u00e0ng 2 c\u1ed9t 3, n\u00f3 c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb b\u1eb1ng 2 v\u00e0 3; t\u01b0\u01a1ng t\u1ef1 15 c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb b\u1eb1ng 3 v\u00e0 5\u2026 N\u1ebfu nh\u01b0 m\u00e1y t\u00ednh c\u1ee7a ch\u00fang ta v\u1ed1n ch\u1ec9 c\u00f3 th\u1ec3 x\u1eed l\u00ed \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 trong v\u00f2ng 15, th\u00ec hi\u1ec7n t\u1ea1i c\u00f3 th\u1ec3 x\u1eed l\u00ed \u0111\u01b0\u1ee3c \u0111\u1ebfn 15. H\u01a1n n\u1eefa, sau khi m\u00e3 h\u00f3a nh\u01b0 v\u1eady thao t\u00e1c c\u0169ng s\u1ebd r\u1ea5t thu\u1eadn ti\u1ec7n.<\/p>\n\n\n\n
V\u00ed d\u1ee5, l\u1ea5y s\u1ed1 2 \u1edf c\u1ed9t hai, l\u1ea5y s\u1ed1 3 \u1edf c\u1ed9t ba, t\u00edch c\u1ee7a ch\u00fang l\u00e0 6, n\u1eb1m \u1edf c\u1ed9t m\u1ed9t. H\u01a1n n\u1eefa, t\u00edch c\u1ee7a b\u1ea5t c\u1ee9 s\u1ed1 n\u00e0o \u1edf c\u1ed9t hai v\u1edbi b\u1ea5t c\u1ee9 s\u1ed1 n\u00e0o \u1edf c\u1ed9t ba c\u0169ng nh\u1ea5t \u0111\u1ecbnh l\u00e0 n\u1eb1m \u1edf c\u1ed9t m\u1ed9t (khi t\u00edch l\u1edbn h\u01a1n 15, c\u00f3 th\u1ec3 ti\u1ebfp t\u1ee5c \u0111i\u1ec1n 16, 17\u2026 v\u00e0o trong h\u00ecnh vu\u00f4ng 3 x 5 d\u1ef1a theo ph\u01b0\u01a1ng ph\u00e1p n\u00f3i tr\u00ean).<\/p>\n\n\n\n
V\u00ec sao l\u1ea1i nh\u01b0 v\u1eady? Th\u00ec ra, trong l\u00ed thuy\u1ebft \u0111\u1ed3ng d\u01b0 th\u1ee9c, n\u1ebfu x1 \u2261 x2 (mod5), y1 \u2261 y2(mod5) (t\u1ee9c x1 v\u00e0 x2 c\u00f3 s\u1ed1 d\u01b0 gi\u1ed1ng nhau sau khi tr\u1eeb \u0111i 5; y1 v\u00e0 y2 c\u00f3 s\u1ed1 d\u01b0 gi\u1ed1ng nhau sau khi tr\u1eeb \u0111i 5), v\u1eady x1y1 \u2261 x2 y2(mod5), c\u0169ng t\u1ee9c l\u00e0 x1y1 v\u00e0 x2 y2 c\u00f3 s\u1ed1 d\u01b0 gi\u1ed1ng nhau sau khi tr\u1eeb \u0111i 5. S\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t n\u00e0y th\u00ec s\u1ebd ch\u1ee9ng minh \u0111\u01b0\u1ee3c, t\u00edch c\u1ee7a s\u1ed1 (c\u00f9ng h\u00e0ng c\u00f3 s\u1ed1 d\u01b0 gi\u1ed1ng nhau sau khi tr\u1eeb \u0111i 5) c\u00f9ng c\u1ed9t v\u1edbi 2 v\u00e0 3 ph\u1ea3i c\u00f3 \u0111\u1ed3ng d\u01b0 6, t\u1ee9c \u1edf c\u00f9ng c\u1ed9t.<\/p>\n\n\n\n
H\u00e0ng \u0111\u1ed1i c\u0169ng c\u00f3 k\u1ebft qu\u1ea3 t\u01b0\u01a1ng t\u1ef1.<\/p>\n\n\n\n
C\u1ee9 nh\u01b0 v\u1eady, m\u00e1y t\u00ednh khi thao t\u00e1c v\u1edbi c\u00e1c s\u1ed1 l\u1edbn s\u1ebd r\u1ea5t thu\u1eadn ti\u1ec7n. Ch\u1eb3ng h\u1ea1n, ch\u00fang ta mu\u1ed1n l\u00e0m ph\u00e9p nh\u00e2n 26, th\u00ec tr\u01b0\u1edbc ti\u00ean ph\u1ea3i ti\u1ebfn h\u00e0nh m\u00e3 h\u00f3a cho hai s\u1ed1: 2 – (h\u00e0ng hai, c\u1ed9t hai) 6 – (h\u00e0ng ba, c\u1ed9t m\u1ed9t)<\/p>\n\n\n\n
C\u00f3 th\u1ec3 ch\u1ee9ng minh, t\u00edch c\u1ee7a s\u1ed1 \u1edf h\u00e0ng hai c\u1ed9t ba ph\u1ea3i \u1edf h\u00e0ng ba; t\u00edch c\u1ee7a s\u1ed1 \u1edf h\u00e0ng hai c\u1ed9t m\u1ed9t ph\u1ea3i \u1edf h\u00e0ng hai. Th\u1ebf l\u00e0, t\u00edch c\u00f3 th\u1ec3 d\u00f9ng 3 v\u00e0 2 \u0111\u1ec3 bi\u1ec3u th\u1ecb (ho\u1eb7c m\u00e3 h\u00f3a). Tra trong b\u1ea3ng s\u1ebd bi\u1ebft \u0111\u01b0\u1ee3c t\u00edch c\u1ee7a 26 l\u00e0 12.<\/p>\n\n\n\n
C\u0169ng c\u00f3 ngh\u0129a l\u00e0, \u0111\u1ea7u ti\u00ean bi\u1ec3u th\u1ecb s\u1ed1 l\u1edbn b\u1eb1ng hai s\u1ed1 nh\u1ecf (c\u00f3 k\u00ed hi\u1ec7u th\u1ee9 t\u1ef1 h\u00e0ng, c\u1ed9t trong b\u1ea3ng); sau \u0111\u00f3 c\u0103n c\u1ee9 theo k\u00ed hi\u1ec7u th\u1ee9 t\u1ef1 c\u1ee7a hai h\u00e0ng \u0111\u1ec3 \u0111\u1ecbnh ra k\u00ed hi\u1ec7u th\u1ee9 t\u1ef1 h\u00e0ng c\u1ee7a t\u00edch hai s\u1ed1 l\u1edbn, c\u0103n c\u1ee9 theo k\u00ed hi\u1ec7u th\u1ee9 t\u1ef1 c\u1ee7a hai c\u1ed9t \u0111\u1ec3 \u0111\u1ecbnh ra k\u00ed hi\u1ec7u th\u1ee9 t\u1ef1 c\u1ed9t c\u1ee7a t\u00edch; cu\u1ed1i c\u00f9ng c\u0103n c\u1ee9 theo k\u00ed hi\u1ec7u th\u1ee9 t\u1ef1 h\u00e0ng v\u00e0 c\u1ed9t trong b\u1ea3ng s\u1ebd tra ra \u0111\u01b0\u1ee3c tr\u1ecb s\u1ed1 c\u1ee7a t\u00edch. Nh\u01b0 v\u1eady, m\u00e1y t\u00ednh s\u1ebd r\u1ea5t d\u1ec5 d\u00e0ng t\u00ecm ra \u0111\u01b0\u1ee3c t\u00edch s\u1ed1 c\u1ee7a c\u00e1c s\u1ed1 l\u1edbn.<\/p>\n\n\n\n
V\u00ec th\u1ebf, vi\u1ec7c s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed th\u1eb7ng d\u01b0 c\u1ee7a Trung Qu\u1ed1c \u0111\u1ec3 ti\u1ebfn h\u00e0nh m\u00e3 h\u00f3a cho m\u00e1y t\u00ednh l\u00e0 h\u1ebft s\u1ee9c h\u1eefu \u00edch, tr\u00ed tu\u1ec7 c\u1ee7a t\u1ed5 ti\u00ean ch\u00fang ta \u0111\u00e3 \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n th\u00eam trong khoa h\u1ecdc k\u0129 thu\u1eadt hi\u1ec7n \u0111\u1ea1i.<\/p>\n\n\n\n
T\u1eeb kh\u00f3a: \u0110\u1ecbnh l\u00fd th\u1eb7ng d\u01b0, \u0111\u1ed3ng d\u01b0, m\u00e3 h\u00f3a.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ch\u00fang ta \u0111\u00e3 bi\u1ebft \u0111\u1ebfn \u0111\u1ecbnh l\u00ed th\u1eb7ng d\u01b0 Trung Qu\u1ed1c, t\u1ee9c v\u1ea5n \u0111\u1ec1 H\u00e0n T\u00edn \u0111i\u1ec3m binh, \u0111\u00f3 l\u00e0 m\u1ed9t th\u00e0nh t\u1ef1u quan tr\u1ecdng trong to\u00e1n h\u1ecdc Trung Qu\u1ed1c c\u1ed5 \u0111\u1ea1i, v\u1edbi n\u1ed9i dung thu\u1ed9c v\u1ec1 gi\u1ea3i ph\u00e1p d\u00e3y \u0111\u1ed3ng d\u01b0 m\u1ed9t l\u1ea7n trong l\u00ed thuy\u1ebft s\u1ed1. Hi\u1ec7n nay, ng\u01b0\u1eddi ta \u0111\u00e3 t\u00ecm 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-7515","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\/7515","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=7515"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7515\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7515"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7515"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}