{"id":1461,"date":"2025-08-02T14:54:26","date_gmt":"2025-08-02T05:54:26","guid":{"rendered":"https:\/\/dept.tus.ac.jp\/st-ma\/?p=1461"},"modified":"2025-08-27T18:02:25","modified_gmt":"2025-08-27T09:02:25","slug":"2025-08-27-%e8%ab%87%e8%a9%b1%e4%bc%9a","status":"publish","type":"post","link":"https:\/\/dept.tus.ac.jp\/st-ma\/2025\/08\/02\/2025-08-27-%e8%ab%87%e8%a9%b1%e4%bc%9a\/","title":{"rendered":"2025.08.27 \u8ac7\u8a71\u4f1a"},"content":{"rendered":"\n<figure class=\"wp-block-table td_to_th_\"><table><tbody style=\"--tbody-th-color--bg:var(--color_main);--tbody-th-color--txt:var(--swl-text_color--white)\"><tr><td>\u8b1b\u6f14\u8005<\/td><td>\u5c0f\u677e\u5c1a\u592b\u6c0f\uff08\u6cb3\u5357\u7701\u79d1\u5b66\u9662\u6570\u5b66\u7814\u7a76\u6240\uff09<\/td><\/tr><tr><td>\u984c\u76ee<\/td><td>The number of primes in a numerical semigroup<\/td><\/tr><tr><td>\u65e5\u6642<\/td><td>2025\u5e748\u670827\u65e5\uff08\u6c34\uff09 16:30 \uff5e17:30<\/td><\/tr><tr><td>\u5834\u6240<\/td><td>\u6771\u4eac\u7406\u79d1\u5927\u5b66\u91ce\u7530\u30ad\u30e3\u30f3\u30d1\u30b94\u53f7\u99283\u968e\u6570\u7406\u79d1\u5b66\u79d1\u30bb\u30df\u30ca\u30fc\u5ba4<\/td><\/tr><tr><td>\u6982\u8981<\/td><td>For two coprime positive integers a and b, let S(a,b) be the set of all integers of the form a u + b v, where u and v are nonnegative integers. It is well known that every integer &gt; a b-a-b is in S(a, b). In this talk, we consider prime numbers less than or equal to a b-a-b, then study the ratio between the number of prime numbers not in S(a,b) and the number of prime numbers in S(a,b). Furthermore, we can give general result for generalized S_l(a,b), that is the set of all integers which can be written in the form a u+b v in more than l ways.<\/td><\/tr><tr><td>\u5171\u50ac<\/td><td>\u5148\u7aef\u7684\u4ee3\u6570\u5b66\u878d\u5408\u7814\u7a76\u90e8\u9580 \u91ce\u7530\u4ee3\u6570\u30bb\u30df\u30ca\u30fc\uff0c<br>\u6570\u7406\u9023\u643a\u30d7\u30ed\u30b8\u30a7\u30af\u30c8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"806\" height=\"604\" src=\"\/upfiles\/sites\/23\/2025\/08\/20250827-komatsu.png\" alt=\"\" class=\"wp-image-1479\" srcset=\"\/upfiles\/sites\/23\/2025\/08\/20250827-komatsu.png 806w, \/upfiles\/sites\/23\/2025\/08\/20250827-komatsu-300x225.png 300w, \/upfiles\/sites\/23\/2025\/08\/20250827-komatsu-768x576.png 768w\" sizes=\"(max-width: 806px) 100vw, 806px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>2025\u5e748\u670827\u65e5\uff08\u6c34\uff09\u306b\u5c0f\u677e\u5c1a\u592b\u6c0f\uff08\u6cb3\u5357\u7701\u79d1\u5b66\u9662\u6570\u5b66\u7814\u7a76\u6240\uff09\u306e\u8ac7\u8a71\u4f1a\u3092\u958b\u50ac\u3057\u307e\u3059\uff0e<\/p>\n","protected":false},"author":125,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"swell_btn_cv_data":"","footnotes":""},"categories":[20,19],"tags":[],"class_list":["post-1461","post","type-post","status-publish","format-standard","hentry","category-algebra2025","category-danwa2025"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.4 - 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