{"id":8160,"date":"2008-09-13T06:55:00","date_gmt":"2008-09-13T06:55:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=8160"},"modified":"2008-09-13T06:55:00","modified_gmt":"2008-09-13T06:55:00","slug":"4t2tk-%eb%ac%b8%ec%a0%9c-%ed%95%b4%ea%b2%b0%ed%96%88%ec%9d%8c","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=8160","title":{"rendered":"4^t=2^t+k \ubb38\uc81c : \ud574\uacb0\ud588\uc74c"},"content":{"rendered":"<div class=\"desc\">\n        *\uc804 \uc138\uacc4\uc5d0\uc11c 248\ubc88\uc9f8\ub85c \ud480\uc5c8\ub2e4. -_-;<br \/>\n        <br \/>\n        \ub2e4 \ud480\uace0\ub098\uc11c \ub0b4 \uc815\ub2f5\uc744 \ud655\uc778\ud558\uae30\ub97c \ubc14\ub780\ub2e4. \uc815\ub2f5\uc740 \uc77c\ub2e8 \uac00\uc7a5 \ub05d\uc5d0\ub2e4\uac00 \uac00\ub824\ub454\ub2e4.<\/p>\n<p>\n        \uc624\ub798\uac04\ub9cc\uc5d0 \uc218\ud559 \ubb38\uc81c\ub97c \ubc1c\uacac\ud588\ub2e4.<\/p>\n<p>        \ubb38\uc81c\uc758 \uc6d0\ubb38\uc740<br \/>\n        <a href=\"http:\/\/projecteuler.net\/index.php?section=problems&#038;id=207\"><br \/>\n         http:\/\/projecteuler.net\/index.php?section=problems&#038;id=207<br \/>\n        <\/a><br \/>\n        \uc5d0\uc11c \ucc3e\uc744 \uc218 \uc788\ub2e4.<\/p>\n<p>        \uc774 \ubb38\uc81c\ub97c \ud480\uae30 \uc704\ud574\uc11c \uace0\uc728\ub2d8\uc758 \uc544\uc774\ub514\uc5b4 \ub300\ub85c $X=2^t$ \ub85c \uce58\ud658\ud55c\ub2e4.<br \/>\n        <br \/>\n        \uadf8\ub7fc \uc8fc\uc5b4\uc9c4 \uc2dd\uc740 $X^2-X-k=0$\uc774\ub77c\ub294 2\ucc28 \ubc29\uc815\uc2dd\uc774 \ub41c\ub2e4. \uc774 2\ucc28 \ubc29\uc815\uc2dd\uc744 \ud480\uc5b4\ubcf4\uc790.<br \/>\n        <br \/>\n        $X=\\frac{1}{2} \\pm \\frac{1}{2}\\sqrt{1+4k}$<br \/>\n        <br \/>\n        \uc774 \ub41c\ub2e4.<br \/>\n        <br \/>\n        \ub2e4\uc2dc X\ub97c \uc6d0\ub798\ub300\ub85c \uce58\ud658\ud558\uba74<br \/>\n        <br \/>\n        $2^t=\\frac{1}{2} \\pm \\frac{1}{2}\\sqrt{1+4k}$<br \/>\n        <br \/>\n        \uc774 \ub41c\ub2e4. \uadf8\ub7f0\ub370 $2^t$\ub294 \uc591\uc218\ubc16\uc5d0 \uc5c6\uc73c\ubbc0\ub85c<br \/>\n        <br \/>\n        $2^t=\\frac{1}{2} + \\frac{1}{2}\\sqrt{1+4k}$<br \/>\n        <br \/>\n        \uc774 \ub420 \uac83\uc774\ub2e4. $2^t$\uac00 \uc815\uc218\uac00 \ub418\uc5b4\uc57c \ud55c\ub2e4\ub294 \uc870\uac74\uc774 \uc788\uc73c\ubbc0\ub85c, \uc6b0\ubcc0\ub3c4 \uc815\uc218\uac00 \ub418\uc5b4\uc57c \ud55c\ub2e4. \uadfc\ub370 \uc815\uc218\uac00 \uc544\ub2cc \uc720\ub9ac\uc218\uc778 1\/2\uac00 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc880 \uace4\ub780\ud574 \ubcf4\uc778\ub2e4. \uc774 \ubd80\ubd84\uc744 \uc99d\uba85\ud558\uace0 \ub118\uc5b4\uac00\uc790. \uc77c\ub2e8 1+4k\uac00 \uc5b4\ub5a4 \uc815\uc218\uc758 \uc81c\uacf1\uc218\uac00 \uc544\ub2c8\ub77c\uace0 \ud558\uc790. \uadf8\ub807\ub2e4\uba74 \uc6b0\ubcc0\uc740 \ubb34\ub9ac\uc218\uac00 \ub418\ubbc0\ub85c, \ubc18\ub4dc\uc2dc 1+4k\ub294 \uc5b4\ub5a4 \uc815\uc218\uc758 \uc81c\uacf1\uc218\uac00 \ub418\uc5b4\uc57c\ub9cc \ud55c\ub2e4. \ub610\ud55c, 1+4k\uac00 \uc5b4\ub5a4 \uc815\uc218\uc758 \uc81c\uacf1\uc218\ub77c\uba74, 1+4k\ub294 \ud640\uc218\uc774\ubbc0\ub85c \uadf8 \uc81c\uacf1\uadfc \uc5ed\uc2dc \ud640\uc218\uc774\ub2e4. \ud640\uc218\uc758 \uc808\ubc18\uc5d0 1\/2\uc744 \ub354\ud558\uba74 \uc815\uc218\uac00 \ub098\uc628\ub2e4. \ub530\ub77c\uc11c 1+4k\uac00 \uc81c\uacf1\uc218\uc774\uae30\ub9cc \ud558\uba74 \ub41c\ub2e4. \uc989, t\uac00 \ud30c\ud2f0\uc158\uc774 \ub420 \uc870\uac74\uc740 1+4k\uac00 \uc81c\uacf1\uc218\uac00 \ub420 \uc870\uac74\uacfc \uac19\ub2e4. \uadf8\ub7fc m\ubcf4\ub2e4 \uc791\uc740 k\uc5d0 \ub300\ud574\uc11c 1+4k\uac00 \uc81c\uacf1\uc218\uc778\uc9c0 \uc870\uc0ac\ud558\uba74 \ub41c\ub2e4.  1+4k\uc758 \uc81c\uacf1\uadfc\uc744 2n+1\uc774\ub77c\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub7fc $1+4k=4n^2+4n+1$ \uc774\ubbc0\ub85c $k=n(n+1)$ \uc774 \ub41c\ub2e4. \uc774 \ub9d0\uc740, $k=n(n+1)$\uc870\uac74\uc744 \ub9cc\uc871\ud558\uae30\ub9cc \ud558\uba74 t\ub294 \ud30c\ud2f0\uc158\uc774 \ub41c\ub2e4\ub294 \ub73b\uc774\ub2e4. \uadf8\ub7fc m\ubcf4\ub2e4 \uc791\uc740 n(n+1)\uc778 \uc22b\uc790\ub4e4\uc744 \ucc3e\uc544\ub0b4\uba74 \ub41c\ub2e4.<\/p>\n<p>\n        \uc774\uc81c, t\uac00 \uc591\uc758 \uc815\uc218(\uc55e\uc73c\ub85c\ub294 \uadf8\ub0e5 \uc815\uc218\ub77c\uace0 \ud558\uaca0\ub2e4)\uc778 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud574 \ubcf4\uc790.<br \/>\n        <br \/>\n        $2^t=\\frac{1}{2} + \\frac{1}{2}\\sqrt{1+4k}$<br \/>\n        <br \/>\n        \uc5ec\uae30\uc5d0 k=n(n+1)\uc744 \ub300\uc785\ud574 \ubcf4\uc790.<br \/>\n        <br \/>\n        $2^t = 1+ 2n+1 = 2(n+1)$<br \/>\n        <br \/>\n        \uc774\ub807\uac8c \uc2dd\uc774 \ubcc0\ud588\ub2e4. \uc55e\uc5d0 \uc788\ub294 2\ub97c \ub5bc\uc5b4 \ub0b4\uace0\ub3c4 t\uac00 \uc815\uc218\uac00 \ub418\uae30 \uc704\ud574\uc11c\ub294 n+1 \ub610\ud55c 2\uc758 \uac70\ub4ed\uc81c\uacf1\uc218\uc774\uba74 \ucda9\ubd84\ud558\ub2e4.<br \/>\n        <br \/>\n        \ub530\ub77c\uc11c t\uac00 perfect partition\uc774 \ub418\uae30 \uc704\ud574\uc11c\ub294 \uc5b4\ub5a4 \uc591\uc758 \uc815\uc218 q\uc5d0 \ub300\ud574\uc11c $n=2^q-1$ \ud615\ud0dc\uba74 \ucda9\ubd84\ud558\ub2e4.<\/p>\n<p>        \uc790, \uc774\uc81c m\uc5d0 \ub300\ud574 t\uac00 \uc815\uc218\uac00 \ub418\ub294 k\uac00 \uba87\uac1c\ub098 \ub418\ub294\uc9c0 \ub530\uc838\ubcfc \ucc28\ub840\ub2e4.<br \/>\n        <br \/>\n        k=n(n+1)\uc774\uc5c8\uace0, $n=2^q-1$ \ud615\ud0dc\uc600\uc73c\ubbc0\ub85c, \uc774\uac78 \ub2e4\uc2dc k\uc5d0 \ub300\uc785\ud558\uba74<br \/>\n        <br \/>\n        $k=4^q-2^q$<br \/>\n        <br \/>\n        \uac00 \ub41c\ub2e4.<br \/>\n        <br \/>\n        \uc774\uc81c, q\uc5d0 1\ubd80\ud130 \ud558\ub098\uc529 \ub300\uc785\ud574 \uac00\uba74\uc11c \ubb38\uc81c\uc5d0\uc11c \uc8fc\uc5b4\uc9c4 m\uc774 k\ubcf4\ub2e4 \uc791\uc740 \uacbd\uc6b0\uac00 \uba87\uac1c\ub098 \ub418\ub294\uc9c0 \ubcf4\uba74 \ub41c\ub2e4.<\/p>\n<p>        \ub530\ub77c\uc11c, \ub2e4\uc74c\uc758 \ubd80\ub4f1\uc2dd\uc744 \ub9cc\uc871\ud558\ub294 \ucd5c\ub300\uc758 q\uac12\uc744 \uad6c\ud558\uba74 \ub41c\ub2e4.<br \/>\n        <br \/>\n        $4^q -2^q \\leq m$<\/p>\n<p>\n        \uc815\ub9ac\ud558\uc790\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n        <br \/>\n        1.n(n+1)\uc774 m\ubcf4\ub2e4 \uc791\uac8c \ub418\ub294 \uc591\uc758 \uc815\uc218 n\uc774 \uba87\uac1c\uc778\uc9c0 \uc870\uc0ac\ud55c\ub2e4. \uc774 \uc22b\uc790\ub97c A(m)\ub77c\uace0 \uc815\uc758\ud55c\ub2e4.<br \/>\n        <br \/>\n        2.\uadf8\ub7ec\ud55c \uc591\uc758 \uc815\uc218 n\uc911\uc5d0\uc11c n+1\uc774 2\uc758 \uac70\ub4ed\uc81c\uacf1\uc218\uac00 \ub418\ub294 \uacbd\uc6b0\uac00 \uba87\uac1c\uc778\uc9c0 \uc870\uc0ac\ud55c\ub2e4. \uc774 \uc22b\uc790\ub97c B(m)\ub77c\uace0 \ud55c\ub2e4.<br \/>\n        <br \/>\n        3. P(m)=A(m)\/B(m) \uc774\ub2e4.<\/p>\n<p>        \uadf8\ub7f0\ub370, \ubc18\ub300\ub85c \uc0dd\uac01\ud574 \ubcf4\uc790. \uc5b4\ucc28\ud53c k\ub294 n(n+1)\uc774 \ub418\uae30\ub9cc \ud558\uba74 \ub418\ubbc0\ub85c, $n=2^q-1$\uc744 \uacc4\uc0b0\ud574\uc11c q\ub97c 1\uc529 \ub354\ud558\uace0, \uadf8\ub54c\ub9c8\ub2e4 n\uc774 \uc5b4\ub5bb\uac8c \ucee4\uc9c0\ub294\uc9c0\ub97c \uc0b4\ud3b4\ubcf4\uba74 \ub418\uc9c0 \uc54a\uc744\uae4c?<\/p>\n<p>        \uc5b4\uca0c\uac70\ub098 \uc774 \ubb38\uc81c\ub97c \ud480\uac8c \ub41c \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n        <br \/>\n        1. n\uc744 \uacc4\uc18d\ud574\uc11c 1\uc529 \ud0a4\uc6cc\ub098\uac04\ub2e4.<br \/>\n        <br \/>\n        2. n+1\uc774 2\uc758 \uac70\ub4ed\uc81c\uacf1\uc218\uac00 \ub418\uba74 q\ub97c 1\ub9cc\ud07c \uc99d\uac00\uc2dc\ud0a8\ub2e4.<br \/>\n        <br \/>\n        3. q\/n<1\/12345\uac00 \ub418\uba74 \uba48\ucd94\uace0 n*(n+1)\uc744 \ucd9c\ub825\ud55c\ub2e4.\n        <br \/>\n        \ucd9c\ub825\ub41c \uac12\uc774 m\uc758 \ucd5c\uc18c\uac12\uc774\ub2e4.<\/p>\n<p>\n        \ub367\ubd99\uc784.<br \/>\n        <br \/>\n        \ubb38\uc81c \ud574\uacb0\ud558\ub294 \ucf54\ub4dc\ub97c C\ub85c \uc9f0\ub294\ub370 32\ube44\ud2b8 \uba38\uc2e0\uc5d0\uc11c \uc4f8 \uc218 \uc788\ub294 \uc22b\uc790\uc758 \uc790\ub9bf\uc218\uac00 \ub108\ubb34 \uc791\uc544\uc11c (\ub2f5\uc774 4294967296\uc744 \ub118\ub294 \uac83 \uac19\uc74c) \ud480\uc9c0 \ubabb\ud558\uc600\ub2e4.<br \/>\n        <br \/>\n        \uc774\uac74 \ubb50 \ud398\ub974\ub9c8\uc758 \ub300\uc815\ub9ac\ub3c4 \uc544\ub2c8\uace0&#8230;-_-;;;;<\/p>\n<p>        \uacb0\ub860\uc801\uc73c\ub85c.<br \/>\n        <br \/>\n        \ub2f5\uc774 32\ube44\ud2b8 \uba38\uc2e0\uc5d0\uc11c \uc4f8 \uc218 \uc788\ub294 \uc22b\uc790(4294967296)\ubcf4\ub2e4 \ub9ce\uc740 \uac83\uc740 \uc0ac\uc2e4\uc774\uc5c8\ub2e4. \uadf8\ub798\uc11c \ub9c8\uc9c0\ub9c9 \uacc4\uc0b0\uc740 \uacf5\ud559\uc6a9 \uacc4\uc0b0\uae30\ub97c \uc37c\ub2e4.<\/p>\n<p>        \uc815\ub2f5<br \/>\n        <\/p>\n<p class=\"moreless_fold\" id=\"more963_0\">\n<span onclick=\"toggleMoreLess(this, '963_0','\uc815\ub2f5\ubcf4\uae30','\uadf8\ub9cc\ubcf4\uae30'); return false;\" style=\"cursor: pointer;\"><br \/>\n          \uc815\ub2f5\ubcf4\uae30<br \/>\n         <\/span>\n<\/p>\n<div class=\"moreless_content\" id=\"content963_0\" style=\"display: none;\">\n         \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 m\uc740 m=44043947822 \uc774\ub2e4.<br \/>\n         \n<\/div>\n<p><\/p>\n<div style=\"width:100%;margin-top:30px;clear:both;height:30px\">\n<div style=\"width:31px;float:left;\">\n<a href=\"\/toolbar\/popup\/abuseReport\/?entryId=963\" onclick=\"window.open(this.href, 'tistoryThisBlogPopup', 'width=550, height=510, toolbar=no, menubar=no, status=no, scrollbars=no'); return false;\"><br \/>\n<img data-recalc-dims=\"1\" decoding=\"async\" alt=\"\uc2e0\uace0\" src=\"https:\/\/i0.wp.com\/t1.daumcdn.net\/tistory_admin\/static\/ico\/ico_spam_report.png\" style=\"border:0\"\/><br \/>\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>*\uc804 \uc138\uacc4\uc5d0\uc11c 248\ubc88\uc9f8\ub85c \ud480\uc5c8\ub2e4. -_-; \ub2e4 \ud480\uace0\ub098\uc11c \ub0b4 \uc815\ub2f5\uc744 \ud655\uc778\ud558\uae30\ub97c \ubc14\ub780\ub2e4. \uc815\ub2f5\uc740 \uc77c\ub2e8 \uac00\uc7a5 \ub05d\uc5d0\ub2e4\uac00 \uac00\ub824\ub454\ub2e4. \uc624\ub798\uac04\ub9cc\uc5d0 \uc218\ud559 \ubb38\uc81c\ub97c \ubc1c\uacac\ud588\ub2e4. \ubb38\uc81c\uc758 \uc6d0\ubb38\uc740 http:\/\/projecteuler.net\/index.php?section=problems&#038;id=207 \uc5d0\uc11c \ucc3e\uc744 \uc218 \uc788\ub2e4. \uc774 \ubb38\uc81c\ub97c \ud480\uae30 \uc704\ud574\uc11c \uace0\uc728\ub2d8\uc758 \uc544\uc774\ub514\uc5b4 \ub300\ub85c $X=2^t$ \ub85c \uce58\ud658\ud55c\ub2e4. \uadf8\ub7fc \uc8fc\uc5b4\uc9c4 \uc2dd\uc740 $X^2-X-k=0$\uc774\ub77c\ub294 2\ucc28 \ubc29\uc815\uc2dd\uc774 \ub41c\ub2e4. \uc774 2\ucc28 \ubc29\uc815\uc2dd\uc744 \ud480\uc5b4\ubcf4\uc790. $X=\\frac{1}{2} \\pm \\frac{1}{2}\\sqrt{1+4k}$ \uc774 \ub41c\ub2e4. \ub2e4\uc2dc X\ub97c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-8160","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-27C","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/8160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8160"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/8160\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8160"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}