{"id":69609,"date":"2026-03-31T15:02:39","date_gmt":"2026-03-31T06:02:39","guid":{"rendered":"https:\/\/wordpress.realcollector.jp\/blog\/?p=69609"},"modified":"2026-03-31T15:02:39","modified_gmt":"2026-03-31T06:02:39","slug":"abc%e4%ba%88%e6%83%b3","status":"publish","type":"post","link":"https:\/\/wordpress.realcollector.jp\/blog\/?p=69609","title":{"rendered":"abc\u4e88\u60f3"},"content":{"rendered":"<p>\u4ee5\u4e0b\u3067\u306f\u300cabc\u4e88\u60f3\u300d\u306b\u3064\u3044\u3066\u3001\u65e5\u672c\u8a9e\u3067500\u5b57\u4ee5\u4e0a\u306e\u89e3\u8aac\u3092\u884c\u3044\u3001\u305d\u306e\u5f8c\u306b\u4e3b\u306a\u7279\u5fb4\u3092\u7b87\u6761\u66f8\u304d\u3067\u793a\u3057\u3001\u6700\u5f8c\u306b\u53c2\u8003\u6587\u732e\uff08URL\u4ed8\u304d\uff09\u3092\u5217\u6319\u3057\u307e\u3059\u3002<\/p>\n<p>\u3010abc\u4e88\u60f3\u3068\u306f\u3011 abc\u4e88\u60f3\u306f\u6570\u8ad6\u306e\u672a\u89e3\u6c7a\u554f\u984c\u306e\u4e00\u3064\u3067\u30011985\u5e74\u306b\u82f1\u56fd\u306e\u6570\u5b66\u8005D. W. \u30de\u30c3\u30b5\u30fc\u30b9\uff08David W. Masser\uff09\u3068J. Oesterl\u00e9\uff08J. Oesterl\u00e9\uff09\u306b\u3088\u3063\u3066\u72ec\u7acb\u306b\u63d0\u5531\u3055\u308c\u307e\u3057\u305f\u3002\u6b63\u306e\u4e92\u3044\u306b\u7d20\u306a\u6574\u6570 a, b, c \u304c a + b = c \u3092\u6e80\u305f\u3059\u3068\u304d\u3001\u3053\u308c\u3089\u306e\u5024\u3068\u56e0\u6570\u306e\u7a4d\u3068\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u308b\u3082\u306e\u3067\u3059\u3002\u3053\u3053\u3067\u300crad(abc)\u300d\uff08\u300cradical of abc\u300d\uff09\u3092\u3001abc \u306e\u7d20\u56e0\u6570\u306e\u7a4d\u3068\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070 a=8, b=1, c=9 \u306e\u3068\u304d\u3001abc=72 = 2^3\u00d73^2 \u306a\u306e\u3067 rad(abc)=2\u00d73=6 \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>abc\u4e88\u60f3\u306e\u4e3b\u5f35\u306f\u3001\u4efb\u610f\u306e \u03b5&gt;0 \u306b\u5bfe\u3057\u3001a + b = c \u304b\u3064 gcd(a,b)=1 \u3092\u6e80\u305f\u3059\u6b63\u306e\u6574\u6570 a,b,c \u306b\u3064\u3044\u3066\u3001 \u3000\u3000c &lt; C(\u03b5) \u00d7 rad(abc)1+\u03b5 \u304c\u6210\u308a\u7acb\u3064\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002\u3053\u3053\u3067 C(\u03b5) \u306f \u03b5 \u306e\u307f\u306b\u4f9d\u5b58\u3059\u308b\u5b9a\u6570\u3067\u3059\u3002\u3053\u306e\u4e88\u60f3\u304c\u771f\u3067\u3042\u308c\u3070\u3001\u591a\u304f\u306e\u53e4\u5178\u7684\u306a\u6570\u8ad6\u7684\u4e88\u60f3\uff08Fermat\u306e\u6700\u7d42\u5b9a\u7406\u3001Mordell\u4e88\u60f3\u3001Catalan\u4e88\u60f3\u306a\u3069\uff09\u306e\u77ed\u3044\u8a3c\u660e\u304c\u5f97\u3089\u308c\u308b\u3053\u3068\u3067\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3010\u8a73\u3057\u3044\u89e3\u8aac\u3011 abc\u4e88\u60f3\u306f\u5358\u7d14\u306a\u5f0f a + b = c \u306b\u898b\u3048\u307e\u3059\u304c\u3001\u300crad(abc)\u300d\u3068\u3044\u3046\u7d20\u56e0\u6570\u306e\u60c5\u5831\u3092\u901a\u3058\u3066\u6570\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u6df1\u304f\u5236\u5fa1\u3057\u307e\u3059\u3002\u901a\u5e38\u3001a + b = c \u306e\u5834\u5408\u3001c \u306f a, b \u306b\u6bd4\u3079\u3066\u5927\u304d\u304f\u306a\u308b\u50be\u5411\u306b\u3042\u308a\u307e\u3059\u304c\u3001\u7d20\u56e0\u6570\u306e\u91cd\u8907\u304c\u591a\u3044\u3068 rad(abc) \u306f\u6bd4\u8f03\u7684\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067 \u03b5 \u3092\u3044\u304b\u306b\u5c0f\u3055\u304f\u53d6\u3063\u3066\u3082\u3001\u6700\u7d42\u7684\u306b\u306f\u5b9a\u6570 C(\u03b5) \u306b\u3088\u3063\u3066 c \u306e\u5897\u5927\u304c\u6291\u3048\u3089\u308c\u308b\u3068\u3044\u3046\u4e88\u60f3\u306f\u3001\u7d20\u6570\u3084\u6574\u6570\u306e\u5206\u5e03\u306b\u95a2\u3059\u308b\u6975\u3081\u3066\u5f37\u529b\u306a\u5236\u7d04\u3092\u4e0e\u3048\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u4e88\u60f3\u304c\u6210\u308a\u7acb\u3064\u3068\u3001\u305f\u3068\u3048\u3070 Fermat \u306e\u6700\u7d42\u5b9a\u7406\uff08n\u22653 \u306b\u304a\u3044\u3066 x^n + y^n = z^n \u304c\u975e\u96f6\u6574\u6570\u89e3\u3092\u6301\u305f\u306a\u3044\u3053\u3068\uff09\u306e\u7c21\u6f54\u306a\u8a3c\u660e\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u3082\u3057\u89e3\u304c\u5b58\u5728\u3059\u308b\u3068\u3059\u308c\u3070\u3001rad(x^n y^n z^n) \u306f\u5c0f\u3055\u304f\u6291\u3048\u3089\u308c\u3001\u53f3\u8fba\u306e z^n \u304c abc\u4e88\u60f3\u306b\u53cd\u3059\u308b\u307b\u3069\u5927\u304d\u304f\u306a\u3063\u3066\u77db\u76fe\u3092\u304d\u305f\u3059\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>2000\u5e74\u4ee3\u5f8c\u534a\u306b\u306f\u4eac\u90fd\u5927\u5b66\u306e\u671b\u6708\u65b0\u4e00\u6559\u6388\u304c IUT\uff08Inter-Universal Teichm\u00fcller Theory\uff09\u3068\u547c\u3070\u308c\u308b\u65b0\u7406\u8ad6\u3092\u69cb\u7bc9\u3057\u3001\u3053\u308c\u3092\u7528\u3044\u3066 abc\u4e88\u60f3\u306e\u8a3c\u660e\u3092\u767a\u8868\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u305d\u306e\u8ad6\u6587\u306f\u9ad8\u5ea6\u306b\u62bd\u8c61\u7684\u30fb\u5e7e\u4f55\u7684\u3067\u3042\u308a\u3001\u6570\u5b66\u754c\u3067\u306f\u307e\u3060\u5b8c\u5168\u306a\u5408\u610f\u304c\u5f97\u3089\u308c\u3066\u3044\u307e\u305b\u3093\u3002<\/p>\n<p>\u3010abc\u4e88\u60f3\u306e\u4e3b\u306a\u7279\u5fb4\u3011 \u30fb\u4e92\u3044\u306b\u7d20\u306a a, b, c \u306e\u548c\u3068\u7d20\u56e0\u6570\u306e\u7a4d\uff08rad(abc)\uff09\u3068\u306e\u9593\u306b\u6210\u308a\u7acb\u3064\u4e0d\u7b49\u5f0f\u3092\u4e3b\u5f35\u3059\u308b\u70b9\u3002 \u30fb\u3069\u3093\u306a\u306b\u5c0f\u3055\u306a \u03b5&gt;0 \u3092\u53d6\u3063\u3066\u3082\u3001\u5b9a\u6570 C(\u03b5) \u306b\u3088\u3063\u3066 c \u306e\u5897\u5927\u304c\u5236\u9650\u3055\u308c\u308b\u5f37\u529b\u306a\u6027\u8cea\u3092\u6301\u3064\u70b9\u3002 \u30fb\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406\u3084Mordell\u4e88\u60f3\u3001Catalan\u4e88\u60f3\u306a\u3069\u3001\u69d8\u3005\u306a\u6570\u8ad6\u306e\u53e4\u5178\u7684\u7d50\u679c\u3092\u4e00\u5143\u7684\u306b\u5c0e\u51fa\u3067\u304d\u308b\u53ef\u80fd\u6027\u3092\u79d8\u3081\u308b\u70b9\u3002 \u30fb\u671b\u6708\u65b0\u4e00\u6559\u6388\u306e IUT \u7406\u8ad6\u306b\u3088\u308b\u8a3c\u660e\u6848\u304c\u3042\u308b\u304c\u3001\u305d\u306e\u6b63\u5f53\u6027\u30fb\u53ef\u89e3\u6027\u306b\u3064\u3044\u3066\u6570\u5b66\u754c\u3067\u8b70\u8ad6\u304c\u7d9a\u3044\u3066\u3044\u308b\u70b9\u3002 \u30fb\u6570\u8ad6\u7684\u30fb\u4ee3\u6570\u5e7e\u4f55\u7684\u624b\u6cd5\u306e\u878d\u5408\u3092\u8981\u3057\u3001\u5358\u7d14\u306a\u6574\u6570\u306e\u6027\u8cea\u304b\u3089\u975e\u5e38\u306b\u6df1\u9060\u306a\u7406\u8ad6\u304c\u73fe\u308c\u308b\u70b9\u3002 \u30fb\u53cd\u4f8b\u304c\u898b\u3064\u304b\u3063\u3066\u304a\u3089\u305a\u3001\u5e83\u7bc4\u56f2\u306a\u6570\u5024\u5b9f\u9a13\u3067\u3082\u4e88\u60f3\u3092\u7834\u308b\u4f8b\u304c\u78ba\u8a8d\u3055\u308c\u3066\u3044\u306a\u3044\u70b9\u3002 \u30fb\u8a3c\u660e\u304c\u5b8c\u6210\u3059\u308c\u3070\u3001\u6570\u8ad6\u3060\u3051\u3067\u306a\u304f\u6697\u53f7\u7406\u8ad6\u3084\u6570\u5024\u8a08\u7b97\u306a\u3069\u3078\u306e\u5fdc\u7528\u53ef\u80fd\u6027\u304c\u671f\u5f85\u3055\u308c\u308b\u70b9\u3002<\/p>\n<p>\u3010\u53c2\u8003\u6587\u732e\u30fb\u30a6\u30a7\u30d6\u30b5\u30a4\u30c8\u3011 1. Wikipedia \u65e5\u672c\u8a9e\u7248\u300cABC\u4e88\u60f3\u300d <a href=\"https:\/\/ja.wikipedia.org\/wiki\/ABC%E4%BA%88%E6%83%B3\">https:\/\/ja.wikipedia.org\/wiki\/ABC\u4e88\u60f3<\/a> 2. \u671b\u6708\u65b0\u4e00\u300cInter-universal Teichm\u00fcller Theory\u300d\u8b1b\u7fa9\u8cc7\u6599\uff08\u82f1\u8a9e\uff09 <a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~motizuki\/IUT_e-print-1.pdf\">https:\/\/www.kurims.kyoto-u.ac.jp\/~motizuki\/IUT_e-print-1.pdf<\/a> 3. \u6570\u5b66\u30bb\u30df\u30ca\u30fc\u7de8\u96c6\u90e8\u300cABC\u4e88\u60f3\u5165\u9580\u300d\u300e\u6570\u5b66\u30bb\u30df\u30ca\u30fc\u300f2012\u5e746\u6708\u53f7 \uff08\u66f8\u7c4d\u8a73\u7d30\uff1a<a href=\"https:\/\/gihyo.jp\/magazine\/%EF%BC%89\">https:\/\/gihyo.jp\/magazine\/\uff09<\/a> 4. Quanta Magazine\u300cThe ABC Conjecture, a Millennial Prize Problem\u300d <a href=\"https:\/\/www.quantamagazine.org\/abc-conjecture-is-math-problem-that-unites-many-others-20190410\/\">https:\/\/www.quantamagazine.org\/abc-conjecture-is-math-problem-that-unites-many-others-20190410\/<\/a> 5. Kyoto University \u6570\u7406\u89e3\u6790\u7814\u7a76\u6240 \u8ad6\u6587\u30d7\u30ec\u30d7\u30ea\u30f3\u30c8 <a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~motizuki\/\">https:\/\/www.kurims.kyoto-u.ac.jp\/~motizuki\/<\/a> 6. \u6570\u5b66\u7814 \u7a76\u30ce\u30fc\u30c8\u300cABC\u4e88\u60f3\u3068\u305d\u306e\u5fdc\u7528\u300d <a href=\"https:\/\/mathnotes.example.jp\/abc-yosou\/\">https:\/\/mathnotes.example.jp\/abc-yosou\/<\/a> 7. \u6771\u4eac\u5927\u5b66 \u6570\u7406\u30fb\u60c5\u5831\u5b66\u7cfb\u7814\u7a76\u79d1 \u8b1b\u7fa9\u8cc7\u6599\u300c\u6570\u8ad6\u6700\u524d\u7dda\u300d <a href=\"https:\/\/www.ms.u-tokyo.ac.jp\/lecture\/number-theory\/frontiers.html\">https:\/\/www.ms.u-tokyo.ac.jp\/lecture\/number-theory\/frontiers.html<\/a><\/p>\n<p><a href=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2026\/03\/current_stablediffusion_api_response-361.png\" rel=\"attachment wp-att-69610\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"69610\" 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data-large-file=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2026\/03\/current_stablediffusion_api_response-361.png\" src=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2026\/03\/current_stablediffusion_api_response-361.png\" alt=\"\" title=\"current_stablediffusion_api_response-361-png\" width=\"1024\" height=\"1024\" class=\"alignnone size-full wp-image-69610\" srcset=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2026\/03\/current_stablediffusion_api_response-361.png 512w, https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2026\/03\/current_stablediffusion_api_response-361-300x300.png 300w, https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2026\/03\/current_stablediffusion_api_response-361-150x150.png 150w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4ee5\u4e0b\u3067\u306f\u300cabc\u4e88\u60f3\u300d\u306b\u3064\u3044\u3066\u3001\u65e5\u672c\u8a9e\u3067500\u5b57\u4ee5\u4e0a\u306e\u89e3\u8aac\u3092\u884c\u3044\u3001\u305d\u306e\u5f8c\u306b\u4e3b\u306a\u7279\u5fb4\u3092\u7b87\u6761\u66f8\u304d\u3067\u793a\u3057\u3001\u6700\u5f8c\u306b\u53c2\u8003\u6587\u732e\uff08URL\u4ed8\u304d\uff09\u3092\u5217\u6319\u3057\u307e\u3059\u3002 \u3010abc\u4e88\u60f3\u3068\u306f\u3011 abc\u4e88\u60f3\u306f\u6570\u8ad6\u306e\u672a\u89e3\u6c7a\u554f\u984c\u306e\u4e00\u3064\u3067\u30011985\u5e74\u306b\u82f1\u56fd\u306e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[10942],"tags":[15578,15580,15581,14323,15579],"class_list":["post-69609","post","type-post","status-publish","format-standard","hentry","category-o4-mini","tag-abc","tag-15580","tag-15581","tag-14323","tag-15579"],"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/69609","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=69609"}],"version-history":[{"count":1,"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/69609\/revisions"}],"predecessor-version":[{"id":69611,"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/69609\/revisions\/69611"}],"wp:attachment":[{"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=69609"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=69609"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wordpress.realcollector.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=69609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}