{"id":2805,"date":"2025-08-19T01:06:05","date_gmt":"2025-08-18T16:06:05","guid":{"rendered":"https:\/\/math-friend.com\/?p=2805"},"modified":"2025-08-20T01:17:34","modified_gmt":"2025-08-19T16:17:34","slug":"%e3%80%90%e4%ba%ac%e9%83%bd%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%912021","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=2805","title":{"rendered":"\u3010\u4eac\u90fd\u5927\u5b66\u5165\u8a66\u3011\u7d20\u6570\u306b\u95a2\u3059\u308b\u30b7\u30f3\u30d7\u30eb\u306a\u6574\u6570\u554f\u984c\uff082021\uff09"},"content":{"rendered":"\n<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n<p class=\"has-border -border02\">\\(p\\)\u304c\u7d20\u6570\u306e\u3068\u304d, \\(p^4+14\\)\u306f\u7d20\u6570\u3067\u306a\u3044\u3053\u3068\u3092\u793a\u305b.<br><span style=\"text-align:right;display:block;\">(2021 \u4eac\u90fd\u5927\u5b66 \u6587\u7cfb [5])<\/span><\/p>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-crease\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\u2460 \\(p=3\\)\u306e\u3068\u304d$$<br>p^4+14=3^4+14=95=5\\times 19<br>$$\u3068\u306a\u308a, \\(p^4+14\\)\u306f\u7d20\u6570\u3067\u306a\u3044.<br><br>\u2461 \\(p\\neq 3\\)\u306e\u3068\u304d<br>\\(p\\)\u306f\u7d20\u6570\u3060\u304b\u3089, \\(p\\neq 3\\)\u306e\u3068\u304d\\(p\\)\u306f\\(3\\)\u306e\u500d\u6570\u3067\u306f\u306a\u3044. \u3088\u3063\u3066, \u6574\u6570\\(n\\)\u3092\u7528\u3044\u3066, $$<br>p=3n\\pm 1<br>$$\u306e\u5f62\u3067\u8868\u305b\u308b. \u3053\u306e\u3068\u304d, $$<br>\\begin{align}<br>p^4+14&amp;=(3n\\pm 1)^4+14\\\\[1.5ex]<br>&amp;=(3n)^4+4\\cdot (3n)^3\\cdot (\\pm 1)+6\\cdot (3n)^2\\cdot (\\pm 1)^2+4\\cdot(3n)\\cdot(\\pm 1)^3+(\\pm 1)^4+14\\\\[1.5ex]<br>&amp;=3\\times\\left(\\pm 27n^4\\pm 9n^3+18n^2\\mp 4n+5 \\right)<br>\\end{align}<br>$$\u3068\u306a\u308a, \\(p^4+14>14\\)\u3088\u308a, \\(p^4+14\\)\u306f3\u3088\u308a\u5927\u304d\u3044\\(3\\)\u306e\u500d\u6570\u3067\u3042\u308b. \u3088\u3063\u3066, \\(p^4+14\\)\u306f\u7d20\u6570\u3067\u306a\u3044.<br><br>\u2460, \u2461\u3088\u308a, \\(p\\)\u304c\u7d20\u6570\u306e\u3068\u304d, \\(p^4+14\\)\u306f\u7d20\u6570\u3067\u306f\u306a\u3044\u3053\u3068\u304c\u793a\u3055\u308c\u305f.<\/p>\n<\/div><\/div>\n\n\n\n<p>youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/g_DXi7O6dds?si=rK3ltaluwiPVswS6\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059. \\(p\\)\u304c\u7d20\u6570\u306e\u3068\u304d, \\(p^4+14\\)\u306f\u7d20\u6570\u3067\u306a\u3044\u3053\u3068\u3092\u793a\u305b. \u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046. \u2460 \\(p=3\\)\u306e\u3068\u304d$$p^4+14=3^4+14=95=5\\times 1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2806,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-2805","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tokimakuru"],"_links":{"self":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/2805","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2805"}],"version-history":[{"count":6,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/2805\/revisions"}],"predecessor-version":[{"id":2812,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/2805\/revisions\/2812"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/media\/2806"}],"wp:attachment":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}