[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/298312#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/298312","headline":"\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u6570 – Wikipedia","name":"\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u6570 – Wikipedia","description":"\u305d\u306e\u4ed6\u306e\u8d85\u81ea\u7136\u6570\u306b\u3064\u3044\u3066\u306f\u300c\u8d85\u81ea\u7136\u6570\u300d\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002 \u6570\u5b66\u306b\u304a\u3051\u308b\u8d85\u81ea\u7136\u6570 (super\u00adnatural number), \u4e00\u822c\u5316\u3055\u308c\u305f\u81ea\u7136\u6570 (generalized natural number) \u3042\u308b\u3044\u306f\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u6570\uff08\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u3059\u3046\u3001\u82f1: Steinitz number\uff09\u306f\u3001\u81ea\u7136\u6570\u306e\u4e00\u3064\u306e\u4e00\u822c\u5316\u3067\u3042\u308b\u3002\u3053\u306e\u8d85\u81ea\u7136\u6570\u306f1910\u5e74\u306b\u30a8\u30eb\u30f3\u30b9\u30c8\u30fb\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\uff08\u82f1\u8a9e\u7248\uff09 \u304c\u4f53\u8ad6\u306b\u95a2\u3059\u308b\u7814\u7a76\u306e\u4e00\u90e8\u3068\u3057\u3066\u7528\u3044\u305f[1]\u3002 \u8d85\u81ea\u7136\u6570 \u03c9 \u3068\u306f\u3001\u3059\u3079\u3066\u306e\u7d20\u6570\u3092\u4e99\u308b\u5f62\u5f0f\u7684\u306a\u7a4d \u03c9=\u220fppnp{displaystyle omega =prod _{p}p^{n_{p}}} \u3067\u3042\u3063\u3066\u3001\u5404","datePublished":"2022-04-27","dateModified":"2022-04-27","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/5f\/Disambig_gray.svg\/25px-Disambig_gray.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/5f\/Disambig_gray.svg\/25px-Disambig_gray.svg.png","height":"19","width":"25"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/298312","about":["Wiki"],"wordCount":1690,"articleBody":"\u305d\u306e\u4ed6\u306e\u8d85\u81ea\u7136\u6570\u306b\u3064\u3044\u3066\u306f\u300c\u8d85\u81ea\u7136\u6570\u300d\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002\u6570\u5b66\u306b\u304a\u3051\u308b\u8d85\u81ea\u7136\u6570 (super\u00adnatural number), \u4e00\u822c\u5316\u3055\u308c\u305f\u81ea\u7136\u6570 (generalized natural number) \u3042\u308b\u3044\u306f\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u6570\uff08\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u3059\u3046\u3001\u82f1: Steinitz number\uff09\u306f\u3001\u81ea\u7136\u6570\u306e\u4e00\u3064\u306e\u4e00\u822c\u5316\u3067\u3042\u308b\u3002\u3053\u306e\u8d85\u81ea\u7136\u6570\u306f1910\u5e74\u306b\u30a8\u30eb\u30f3\u30b9\u30c8\u30fb\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\uff08\u82f1\u8a9e\u7248\uff09 \u304c\u4f53\u8ad6\u306b\u95a2\u3059\u308b\u7814\u7a76\u306e\u4e00\u90e8\u3068\u3057\u3066\u7528\u3044\u305f[1]\u3002  \u8d85\u81ea\u7136\u6570 \u03c9 \u3068\u306f\u3001\u3059\u3079\u3066\u306e\u7d20\u6570\u3092\u4e99\u308b\u5f62\u5f0f\u7684\u306a\u7a4d \u03c9=\u220fppnp{displaystyle omega =prod _{p}p^{n_{p}}} \u3067\u3042\u3063\u3066\u3001\u5404 np \u304c\u96f6\u3001\u81ea\u7136\u6570\u3001\u221e\u306e\u4f55\u308c\u304b\u3068\u306a\u3063\u3066\u3044\u308b\u3088\u3046\u306a\u3082\u306e\u3092\u8a00\u3046\u3002np \u306f\u3057\u3070\u3057\u3070 vp(\u03c9) \u3068\u3082\u66f8\u304b\u308c\u308b\u3002np = \u221e \u3068\u306a\u308b p \u304c\u7121\u304f\u3001\u304b\u3064\u6709\u9650\u500b\u306e\u4f8b\u5916\u3092\u9664\u304f\u5168\u3066\u306e np \u304c\u96f6\u3068\u306a\u308b\u306a\u3089\u3070\u3001\u3053\u306e\u8d85\u81ea\u7136\u6570\u306f\u6b63\u6574\u6570\u3068\u3044\u3046\u610f\u5473\u3067\u306e\u901a\u5e38\u306e\u81ea\u7136\u6570\u3092\u8868\u3059\u3082\u306e\u3068\u7406\u89e3\u3067\u304d\u308b\u3002\u3084\u3084\u76f4\u89b3\u304b\u3089\u306f\u5916\u308c\u308b\u304c\u3001\u3059\u3079\u3066\u306e p \u306b\u5bfe\u3057\u3066 np = \u221e \u3068\u306a\u308b\u3068\u304d\u3001\u305d\u306e\u8d85\u81ea\u7136\u6570\u306f 0 \u3092\u8868\u3059\u3082\u306e\u3068\u3059\u308b\u3002\u3053\u306e\u8d85\u81ea\u7136\u6570\u306e\u6982\u5ff5\u306f\u3001\u300c\u7121\u9650\u500b\u306e\u7d20\u56e0\u6570\u3092\u6301\u3064\u3053\u3068\u304c\u3067\u304d\u308b\u300d\u300c\uff08\u5bfe\u5fdc\u3059\u308b\u51aa\u6307\u6570\u304c \u221e \u3068\u3059\u308c\u3070\uff09\u4efb\u610f\u306b\u4e0e\u3048\u3089\u308c\u305f\u7d20\u6570\u3067\u201c\u7121\u9650\u56de\u201d\u5272\u308a\u5207\u308c\u308b\u300d\u3068\u3044\u3063\u305f\u72b6\u6cc1\u3092\u8a31\u5bb9\u3059\u308b\u3068\u3044\u3046\u70b9\u3067\u3001\u901a\u5e38\u306e\u81ea\u7136\u6570\u3088\u308a\u3082\u62e1\u5f35\u3055\u308c\u305f\u53d6\u308a\u6271\u3044\u304c\u3067\u304d\u308b\u3002  \u8d85\u81ea\u7136\u6570\u306e\u9593\u306e\u81ea\u7136\u306a\u52a0\u6cd5\u3068\u3044\u3046\u3082\u306e\u306f\u5b58\u5728\u3057\u306a\u3044\u304c\u3001\u4e57\u6cd5\u306f\u5358\u7d14\u306b (\u220fppnp)\u22c5(\u220fppmp):=\u220fppnp+mp{displaystyle (prod _{p}p^{n_{p}})cdot (prod _{p}p^{m_{p}}):=prod _{p}p^{n_{p}+m_{p}}} \u3068\u3059\u308b\u3053\u3068\u3067\u5b9a\u7fa9\u3067\u304d\u308b\u3002\u540c\u69d8\u306b \u03c91\u2223\u03c92:\u27favp(\u03c91)\u2264vp(\u03c92)(\u2200p){displaystyle omega _{1}mid omega _{2}:!iff v_{p}(omega _{1})leq v_{p}(omega _{2})quad (forall p)} \u3068\u3059\u308b\u3053\u3068\u3067\u6574\u9664\u53ef\u80fd\u6027\u3082\u8d85\u81ea\u7136\u6570\u306b\u5bfe\u3057\u3066\u62e1\u5f35\u3067\u304d\u3001\u6700\u5c0f\u516c\u500d\u6570\u3084\u6700\u5927\u516c\u7d04\u6570\u3082 lcm\u2061({\u03c9i}):=\u220fppsup(vp(\u03c9i)),gcd\u2061({\u03c9i}):=\u220fppinf(vp(\u03c9i)){displaystyle operatorname {lcm} ({omega _{i}}):=prod _{p}p^{sup(v_{p}(omega _{i}))},quad operatorname {gcd} ({omega _{i}}):=prod _{p}p^{inf(v_{p}(omega _{i}))}} \u306b\u3088\u3063\u3066\u4e00\u822c\u5316\u3067\u304d\u308b\u3002\u3053\u308c\u3089\u5b9a\u7fa9\u306e\u3082\u3068\u3067\u3001\u7121\u9650\u500b\u306e\u81ea\u7136\u6570\uff08\u3042\u308b\u3044\u306f\u8d85\u81ea\u7136\u6570\uff09\u306b\u5bfe\u3059\u308b gcd \u3084 lcm \u306f\u8d85\u81ea\u7136\u6570\u306e\u7bc4\u56f2\u3067\u5fc5\u305a\u3068\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002  \u81ea\u7136\u6570\u306b\u5bfe\u3059\u308b\u901a\u5e38\u306ep-\u9032\u4ed8\u5024\uff08\u4f4d\u6570\uff09\u51fd\u6570\u3082\u3001\u5404 p \u306b\u5bfe\u3059\u308b vp(\u03c9) = np \u306b\u3088\u3063\u3066\u8d85\u81ea\u7136\u6570\u307e\u3067\u62e1\u5f35\u3067\u304d\u308b\u3002\u8d85\u81ea\u7136\u6570\u306f\u3001\u526f\u6709\u9650\u7fa4\u304a\u3088\u3073\u305d\u306e\u90e8\u5206\u7fa4\u306e\u4f4d\u6570\u304a\u3088\u3073\u6307\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u306b\u7528\u3044\u3089\u308c\u3001\u305d\u308c\u306b\u3088\u308a\u6709\u9650\u7fa4\u8ad6\u306b\u304a\u3051\u308b\u591a\u304f\u306e\u5b9a\u7406\u304c\u305d\u306e\u307e\u307e\u306e\u5f62\u3067\u305d\u308c\u3089\u306e\u7fa4\u306b\u95a2\u3059\u308b\u5b9a\u7406\u3068\u3057\u3066\u6301\u3061\u8fbc\u3081\u308b\u3002\u305d\u308c\u3089\u306f\u6709\u9650\u4f53\u306e\u4ee3\u6570\u62e1\u5927\u3092\u6349\u3048\u308b\u3053\u3068\u306b\u5229\u7528\u3067\u304d\u308b[2]\u3002\u307e\u305f\u3001\u7121\u5e73\u65b9\u6570\u306e\u5bc6\u5ea6\u3084\u5947\u5b8c\u5168\u6570\u306e\u4e0a\u754c\u306a\u3069\u306e\u6570\u8ad6\u7684\u8a3c\u660e\u306e\u591a\u304f\u3067\u6697\u306b\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u3002[\u8981\u51fa\u5178]Table of Contents\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u6ce8\u91c8[\u7de8\u96c6]\u51fa\u5178[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u6ce8\u91c8[\u7de8\u96c6]\u51fa\u5178[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/298312#breadcrumbitem","name":"\u30b7\u30e5\u30bf\u30a4\u30cb\u30c3\u30c4\u6570 – Wikipedia"}}]}]