{"id":4715,"date":"2020-06-01T16:43:42","date_gmt":"2020-06-01T07:43:42","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?p=4715"},"modified":"2021-02-10T18:01:18","modified_gmt":"2021-02-10T09:01:18","slug":"math-1-gauss-lemma-factorization","status":"publish","type":"post","link":"https:\/\/sasamath.com\/blog\/articles\/math-1-gauss-lemma-factorization\/","title":{"rendered":"\uc815\uc218\uacc4\uc218 \ub2e4\ud56d\uc2dd\uc758 \uc778\uc218\ubd84\ud574\uc640 Gauss\uc758 \ubcf4\uc870\uc815\ub9ac"},"content":{"rendered":"

\n\uac00\uc6b0\uc2a4\uc758 \ubcf4\uc870\uc815\ub9ac\uc5d0 \uad00\ud55c \uc9c8\ubb38\uc774 Share Your Math\uc5d0 \uc788\uc5b4\uc11c \uc774\uc5d0 \ub300\ud574 \uc18c\uac1c\ud558\uace0\uc790 \ud569\ub2c8\ub2e4. \u2018\uac00\uc6b0\uc2a4\uc758 \uc815\ub9ac\u2019\ub77c\uace0 \ub9d0\ud558\uba74 \uadf8 \uc885\ub958\uac00 \ub108\ubb34 \ub9ce\uc544\uc11c \ubb34\uc5c7\uc744 \uc77c\uceeb\ub294\uc9c0 \ud63c\ub3d9\uc758 \uc5ec\uc9c0\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uc9c0\uae08 \uc0b4\ud3b4\ubcf4\uace0\uc790 \ud558\ub294 \uac00\uc6b0\uc2a4\uc758 \ubcf4\uc870\uc815\ub9ac\ub294, \ubb3c\ub860, \uc9c8\ubb38\uacfc \uad00\ub828\uc788\ub294 \ub2e4\ud56d\uc2dd\uc758 \uc778\uc218\ubd84\ud574\uc640 \uad00\ub828\ub41c \uc815\ub9ac\uc785\ub2c8\ub2e4.\n<\/p>\n

\n\ub2ec\ube5b\ud559\uc0ac Share Your Math \uac8c\uc2dc\ud310\uc5d0 \uc62c\ub77c\uc628 \uc9c8\ubb38\uc758 \uc694\uc9c0\ub294<\/p>\n

\n\t \uc815\uc218\uacc4\uc218 \ub2e4\ud56d\uc2dd\uc774 (\ucc28\uc218\uac00 \ub354 \ub0ae\uc740) \uc720\ub9ac\uacc4\uc218 \ub2e4\ud56d\uc2dd \ub450 \uac1c\ub85c \uc778\uc218\ubd84\ud574\ub420 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc774 \uadf8 \ub2e4\ud56d\uc2dd\uc774 (\ucc28\uc218\uac00 \ub354 \ub0ae\uc740) \uc815\uc218\uacc4\uc218 \ub2e4\ud56d\uc2dd \ub450 \uac1c\ub85c \uc778\uc218\ubd84\ud574\ub418\ub294 \uac83\uc784\uc744 \uc5b4\ub5bb\uac8c \uc99d\uba85\ud560 \uc218 \uc788\ub294\uac00?\n<\/p><\/blockquote>\n

\uc785\ub2c8\ub2e4. \uc778\uc218\ubd84\ud574\ub97c \uc12c\uc138\ud558\uac8c \uc0b4\ud3b4\ubcf8 \ud559\uc0dd\uc740 \uc704\uc758 \uc9c8\ubb38\uc5d0 \uc5b8\uae09\ub41c \uc0ac\uc2e4\uc744 \uc5b4\ub290 \uc815\ub3c4 \ucd94\uce21\ud560 \uc218 \uc788\uc5c8\uc744 \uc218\ub3c4 \uc788\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \uc0ac\uc2e4\uc744 \uc99d\uba85\ud558\ub294 \ub370\uc5d0 \ubc14\ub85c \uac00\uc6b0\uc2a4\uc758 \ubcf4\uc870\uc815\ub9ac\uac00 \uc0ac\uc6a9\ub429\ub2c8\ub2e4.\n<\/p>\n

\n\uc774 \uc815\ub9ac\ub294 \ubcf4\ud1b5 \uc218\ud559\uacfc \ud559\ubd80\uacfc\uc815 \uc911 \ud558\ub098\uc778 \ub300\uc218\ud559 \uc218\uc5c5\uc5d0\uc11c \ub4f1\uc7a5\ud569\ub2c8\ub2e4. \uadf8\ub798\uc11c \uad00\ub828 \ub0b4\uc6a9\uc740 \ubb3c\ub860 \uc77c\ubc18\uc801\uc778 \ub300\uc218\ud559 \uad50\uc7ac\uc5d0 \uc798 \uc815\ub9ac\ub418\uc5b4 \uc788\ub294\ub370\uc694, \uc544\ubb34\ub798\ub3c4 \ub300\ud559\uad50 \ub300\uc218\ud559 \uad50\uc7ac\uc774\ub2e4\ubcf4\ub2c8 \uc880 \ub354 \uc77c\ubc18\uc801\uc778 \uc218\uccb4\uacc4 \uc704\uc5d0\uc11c\uc758 \uc0c1\ud669\uc744 \uc5fc\ub450\ud574 \ub454 \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\ud0dc\ub85c \uae30\uc220\ub418\uc5b4 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n

\n

\n\t\t\ubcf4\uc870\uc815\ub9ac 1. (\uac00\uc6b0\uc2a4 \ubcf4\uc870\uc815\ub9ac – \ub300\ud559\uc0dd \ubc84\uc804)<\/span><\/p>\n

\\(D\\)\uac00 \uc720\uc77c\ubd84\ud574\uc815\uc5ed(UFD; unique factorization domain)\uc774\uba74, \\(D[x]\\)\uc758 \ub450 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc758 \uacf1\uc740 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ub2e4.\n<\/p>\n<\/div>\n

\n\uc720\uc77c\ubd84\ud574\uc815\uc5ed<\/span>\uc774\ub780 \ub300\ucda9 \ub9d0\ud558\uba74, \\((\\mathbb{Z}, +, \\cdot)\\), \uc989 \uc815\uc218\uc804\uccb4 \uc9d1\ud569\uc744 \uc77c\ubc18\ud654\ud55c \uac83\uc785\ub2c8\ub2e4. \\(D[x]\\)\ub294 \\(D\\)\uc758 \uc6d0\uc18c\ub97c \uacc4\uc218\ub85c \uac16\ub294 \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \ubaa8\uc784\uc785\ub2c8\ub2e4. \uadf8\ub9ac\uace0 \u2018\\(D\\)\uac00 \uc720\uc77c\ubd84\ud574\uc815\uc5ed\uc774\ub2e4.\u2019\ub77c\ub294 \ub9d0\uc758 \ub73b\uc740 \\(D\\)\uc758 \\(0\\)\uc774 \uc544\ub2cc \uc784\uc758\uc758 \uc6d0\uc18c\ub4e4\uc758 \uc18c\uc778\uc218\ubd84\ud574\uac00 \uc720\uc77c\ud558\uac8c \ub41c\ub2e4\ub294 \ub73b\uc785\ub2c8\ub2e4.<\/span>1<\/sup><\/a><\/span> \uadf8\ub9ac\uace0 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ub780 \ub2e4\ud56d\uc2dd\uc758 \uacc4\uc218\ub4e4\uc774 \uc11c\ub85c\uc18c\ub77c\ub294 \ub73b\uc785\ub2c8\ub2e4. \uc720\uc77c\ubd84\ud574\uc815\uc5ed\uc744 \uac04\ub2e8\ud788 UFD\ub85c \uc501\ub2c8\ub2e4.\n<\/p>\n

\n\uadf8\ub7ec\uba74 \uc704\uc758 \uac00\uc6b0\uc2a4 \ubcf4\uc870\uc815\ub9ac\ub97c \uc774\uc81c \uc911\uace0\ub4f1\ud559\uc0dd
\n \ubc84\uc804\uc73c\ub85c \ubc14\uafb8\uc5b4 \uc99d\uba85\ud574\ubcf4\uace0, \uac00\uc6b0\uc2a4 \ubcf4\uc870\uc815\ub9ac\ub97c \ud65c\uc6a9\ud558\uc5ec \ub2ec\ube5b\ud559\uc0ac\uc5d0 \uc62c\ub77c\uc628 \uc9c8\ubb38\uc5d0 \ub300\ud55c \ub2f5\ubcc0\ub3c4 \ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uba3c\uc800 \uba87\uac00\uc9c0 \ud45c\uae30\uc640 \uc6a9\uc5b4\ub97c \uc815\uc758\ud558\uaca0\uc2b5\ub2c8\ub2e4. \\(\\mathbb{Z}, \\mathbb{Q}\\) \uac01\uac01\uc744 (\ub298 \uadf8\ub798\uc654\ub4ef\uc774) \uc815\uc218 \uc804\uccb4\uc9d1\ud569, \uc720\ub9ac\uc218 \uc804\uccb4\uc9d1\ud569\uc774\ub77c \ud558\uaca0\uc2b5\ub2c8\ub2e4. \uadf8\ub9ac\uace0 \\(\\mathbb{Z}[x], \\mathbb{Q}[x]\\)\ub97c \uac01\uac01 \uc815\uc218 \uacc4\uc218 \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569, \uc720\ub9ac\uc218 \uacc4\uc218 \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569\uc774\ub77c \ud558\uaca0\uc2b5\ub2c8\ub2e4.\n<\/p>\n

\n\ub2e4\uc74c\uc73c\ub85c \u2018\uc815\uc218 \uacc4\uc218 \ub2e4\ud56d\uc2dd
\n\\[f(x)=a_0+a_1x+\\cdots + a_nx^n \\]
\n\uc774 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd<\/span>\uc774\ub2e4\u2019\ub77c\ub294 \ub9d0\uc758 \ub73b\uc740 \\(n+1\\)\uac1c\uc758 \uc815\uc218 \\(a_0, a_1, \\ldots, a_n\\)\uc758 \ucd5c\ub300\uacf5\uc57d\uc218\uac00 \\(1\\)\uc774\ub77c\ub294 \uac83\uc73c\ub85c \uc57d\uc18d\ud558\uaca0\uc2b5\ub2c8\ub2e4. (\ucd5c\ub300\uacf5\uc57d\uc218\uac00 \ubb34\uc5c7\uc778\uc9c0\ub294 \ub530\ub85c \uc57d\uc18d \uc548\ud574\ub3c4 \ub418\uaca0\uc8e0?)\n<\/p>\n

\n\uc774\uc81c \ub2e4\uc74c \ubcf4\uc870\uc815\ub9ac\ub97c \uc99d\uba85\ud574 \ubcf4\uc8e0.\n<\/p>\n

\n

\n\t\t\ubcf4\uc870\uc815\ub9ac 2. (\uac00\uc6b0\uc2a4 \ubcf4\uc870\uc815\ub9ac – \uc911\uace0\ub4f1\ud559\uc0dd \ubc84\uc804)<\/span><\/p>\n

\n\t\\(\\mathbb{Z}[x]\\)\uc758 \ub450 \uc6d0\uc18c \\(f(x), g(x)\\)\uac00 \ubaa8\ub450 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\uba74 \\(f(x)g(x)\\)\ub3c4 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ub2e4.\n<\/p>\n<\/div>\n

\n

\uc99d\uba85<\/p>\n

\n\t\\(f(x)\\)\uc640 \\(g(x)\\)\ub97c \uac01\uac01
\n\t\\[\\begin{align}
\n\tf(x)&=a_0+\\cdots + a_nx^n,\\\\[8pt] g(x)&=b_0+\\cdots b_mx^m
\n\t\\end{align}\\]
\n\t\uc73c\ub85c \ub450\uc790. \uc784\uc758\uc758 \uc18c\uc218 \\(p\\)\ub97c \ud558\ub098 \ud0dd\ud558\uba74, \\(f(x)\\)\uc640 \\(g(x)\\)\uac00 \ubaa8\ub450 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ubbc0\ub85c \\(p\\)\ub294 \ubaa8\ub4e0 \\(a_i\\)\ub4e4\uc744 \ub098\ub20c \uc218\ub294 \uc5c6\uc73c\uba70, \ubaa8\ub4e0 \\(b_i\\)\ub4e4\uc744 \ub098\ub20c \uc218\ub3c4 \uc5c6\ub2e4(\uc608\ub97c \ub4e4\uc5b4 \\(p\\)\uac00 \ubaa8\ub4e0 \\(a_i\\)\ub4e4\uc744 \ub098\ub208\ub2e4\uba74, \\(a_i\\)\ub4e4\uc758 \ucd5c\ub300\uacf5\uc57d\uc218\ub294 \\(p\\)\uc758 \ubc30\uc218\uac00\ub418\uc5b4 \\(f(x)\\)\uac00 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ub77c\ub294 \uac00\uc815\uc5d0 \ubaa8\uc21c\uc774\ub2e4).\n<\/p>\n

\n\\(a_0\\)\ubd80\ud130 \\(a_n\\)\uae4c\uc9c0 \uc77c\ub82c\ub85c \ub098\uc5f4\ud574 \ub450\uace0, \\(p\\)\uac00 \ub098\ub204\uc9c0 \uc54a\ub294 \uccab \ubc88\uc9f8 \uac83\uc744 \\(a_r\\)\uc774\ub77c \ud558\uc790. \uc989 \\(i< r\\)\uc774\uba74 \\(p\\)\uac00 \\(a_i\\)\ub97c \ub098\ub204\uace0, \\(p\\)\ub294 \\(a_r\\)\uc744 \ub098\ub204\uc9c0 \ubabb\ud55c\ub2e4\uace0 \ud558\uc790. \ub9c8\ucc2c\uac00\uc9c0\ub85c \\(p\\)\uac00 \ub098\ub204\uc9c0 \uc54a\ub294 \uccab \ubc88\uc9f8 \\(g(x)\\)\uc758 \uacc4\uc218\ub97c \\(b_s\\)\ub77c \ud558\uc790. \uadf8\ub7ec\uba74\n\t\\(h(x)=f(x)g(x)\\)\uc758 \ud56d \uc911\uc5d0 \\(x^{r+s}\\)\uc758 \uacc4\uc218\ub294\n\t\\[(a_0b_{r+s}+\\cdots +a_{r-1}b_{s+1})+a_rb_s+(a_{r+1}b_{s-1}+\\cdots +a_{r+s}b_0) \\]\n\t\uc778\ub370, \\(p\\)\ub294 \\((a_0b_{r+s}+\\cdots +a_{r-1}b_{s+1})\\)\uc640 \\((a_{r+1}b_{s-1}+\\cdots +a_{r+s}b_0)\\)\ub97c \ubaa8\ub450 \ub098\ub204\uc9c0\ub9cc \\(p\\)\ub294 \\(a_rb_s\\)\ub97c \ub098\ub20c\uc218\ub294 \uc5c6\ub2e4. \n\uc989 \\(p\\)\ub294 \\(x^{r+s}\\)\uc758 \uacc4\uc218\ub97c \ub098\ub204\uc9c0 \uc54a\ub294\ub2e4. \uc5ec\uae30\uc11c \\(p\\)\ub294 \uc784\uc758\uc758 \uc18c\uc218\uc774\ub2e4. \uc989 \uc784\uc758\uc758 \uc18c\uc218\uc5d0 \ub300\ud558\uc5ec \\(h(x)\\)\uc5d0\ub294 \uadf8 \uc18c\uc218\uac00 \ub098\ub20c \uc218 \uc5c6\ub294 \uacc4\uc218\uac00 \uc788\ub2e4. \ub530\ub77c\uc11c \\(h(x)\\)\ub294 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ub2e4.\n<\/span><\/p>\n<\/div>\n

\n\ub9d0\ub9cc \uae38\uac8c \ub298\uc5b4\uc37c\uc9c0, \uc704\uc758 \ub0b4\uc6a9\uc740 \uc911\ud559\uad50 1\ud559\ub144(\ud639\uc740 \ucd08\ub4f1\ud559\uad50)\uc5d0\uc11c \ubc30\uc6b4 \uc57d\uc218, \ubc30\uc218, \ucd5c\ub300\uacf5\uc57d\uc218 \ub0b4\uc6a9\ubfd0\uc785\ub2c8\ub2e4(\uc911\uace0\ub4f1\ud559\uc0dd \ubc84\uc804\uc774\ub77c\ub294 \ub9d0\uc5d0 \ub3d9\uc758\ud560 \uc218 \uc788\uaca0\uc8e0?). \uc774\uc81c \uc704\uc758 \ubcf4\uc870\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c\uc758 main theorem\uc744 \uc99d\uba85\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.\n<\/p>\n

\n

\n\t\t\uc815\ub9ac 3.<\/span>
\n\t\\(f(x)\\in \\mathbb{Z}[x]\\)\uac00 \ucc28\uc218\uac00 \\(1\\) \uc774\uc0c1\uc778 \ub2e4\ud56d\uc2dd\uc774\ub77c \ud558\uc790. \\(f(x)\\)\uac00 \\(f(x)\\)\uc758 \ucc28\uc218\ubcf4\ub2e4 \ub354 \ub0ae\uc740 \ucc28\uc218\uc778 \\(r\\)\uacfc \\(s\\)\ub97c \ucc28\uc218\ub85c \uac16\ub294 \\(\\mathbb{Q}[x]\\)\uc758 \ub450 \ub2e4\ud56d\uc2dd\uc73c\ub85c \uc778\uc218\ubd84\ud574\ub418\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(f(x)\\)\uac00 \ucc28\uc218\uac00 \\(r\\)\uacfc \\(s\\)\uc778 \\(\\mathbb{Z}[x]\\)\uc758 \ub450 \ub2e4\ud56d\uc2dd\uc73c\ub85c \uc778\uc218\ubd84\ud574\ub418\ub294 \uac83\uc774\ub2e4.\n<\/p>\n<\/div>\n

\n\uc544, \uc774 \uba54\uc778 \uc815\ub9ac\uc758 \uc99d\uba85\uc744 \ubc14\ub85c \ud558\ub824\uace0\ubcf4\ub2c8 \ub2e4\ub978 \ubcf4\uc870\uc815\ub9ac\ub97c \ud558\ub098 \uc368\ub450\uace0 \uadf8 \ubcf4\uc870\uc815\ub9ac\ub97c \uc774\uc6a9\ud574\uc11c \uba54\uc778 \uc815\ub9ac\uc758 \uc99d\uba85\uc744 \uc4f0\ub294\uac8c \uc88b\uc740 \uac83 \uac19\uc2b5\ub2c8\ub2e4. \ubcf4\uc870 \uc815\ub9ac\ub97c \ud558\ub098 \ub354 \uc4f0\uaca0\uc2b5\ub2c8\ub2e4.\n<\/p>\n

\n

\n\t\t\ubcf4\uc870\uc815\ub9ac 4.<\/span>
\n\t\ucc28\uc218\uac00 \\(1\\) \uc774\uc0c1\uc778 \ub2e4\ud56d\uc2dd \\(f(x)\\in \\mathbb{Z}[x]\\)\uc5d0 \ub300\ud558\uc5ec \uc801\ub2f9\ud55c \uc815\uc218 \\(c\\)\uc640 \uc801\ub2f9\ud55c \uc6d0\uc2dc\ub2e4\ud56d\uc2dd \\(g(x)\\in\\mathbb{Z}[x]\\)\uac00 \uc874\uc7ac\ud574\uc11c \\(f(x)=cg(x)\\)\ub85c \uc4f8 \uc218 \uc788\ub2e4. \uc774\ub54c \\(c\\)\uc640 \\(g(x)\\)\ub294 \ubd80\ud638\ub97c \ubb34\uc2dc\ud558\uba74 \uc720\uc77c\ud558\ub2e4.\n<\/p>\n<\/div>\n

\n\uc774 \ubcf4\uc870\uc815\ub9ac\ub294 \\(c\\)\uac00 \uc0ac\uc2e4\uc0c1 \\(f(x)\\)\uc758 \uacc4\uc218\ub4e4\uc758 \ucd5c\ub300\uacf5\uc57d\uc218\uc784\uc744 \uc0dd\uac01\ud558\uba74, \uc544\uc8fc \uc790\uba85\ud574\ubcf4\uc785\ub2c8\ub2e4. \uadf8\ub7ec\ub2c8\uae4c \uc774 \ubcf4\uc870\uc815\ub9ac\uc758 \uc99d\uba85\uc740 \uc0dd\ub7b5\ud558\uace0 \uba54\uc778 \uc815\ub9ac\uc758 \uc99d\uba85\uc744 \ud574\ubd05\uc2dc\ub2e4.\n<\/p>\n

\n

\uc815\ub9ac 3\uc758 \ucda9\ubd84\uc870\uac74 \uc99d\uba85.<\/span><\/p>\n

\t\\(f(x)\\in\\mathbb{Z}[x]\\)\uc758 \ucc28\uc218\uac00 \\(1\\) \uc774\uc0c1\uc774\uace0, \\(f(x)\\)\ubcf4\ub2e4 \ucc28\uc218\uac00 \ub0ae\uc740 \\(\\mathbb{Q}[x]\\)\uc758 \ub450 \ub2e4\ud56d\uc2dd \\(r(x), s(x)\\)\uac00 \uc874\uc7ac\ud574\uc11c
\n\t\\[ f(x)=r(x)s(x)\\]
\n\t\ub85c \ub098\ud0c0\ub0b4\uc5b4\uc9c4\ub2e4\uace0 \ud558\uc790. \\(r(x)\\)\uc640 \\(s(x)\\)\uc758 \uacc4\uc218\ub294 \ubaa8\ub450 \\(\\frac{a}{b}\\ (a, b\\in\\mathbb{Z})\\)\uaf34\uc774\uba70 \ub530\ub77c\uc11c \uc801\ub2f9\ud55c \uc815\uc218 \\(d\\in\\mathbb{Z}\\)\ub97c \\(f(x)=r(x)s(x)\\)\uc758 \uc591\ubcc0\uc5d0 \uacf1\ud558\uc5ec \ubd84\ubaa8\ub97c \uc5c6\uc568 \uc218 \uc788\ub2e4. \uc989
\n\t\\begin{align*}
\n\t& d\\cdot f(x)=r_1(x) s_1(x),\\\\[8pt]
\n\t& r_1(x)\\in\\mathbb{Z}[x],\\ s_1(x)\\in\\mathbb{Z}[x],\\\\[8pt]
\n\t& \\deg r(x)=\\deg r_1(x),\\ \\deg s(x)=\\deg s_1(x)
\n\t\\end{align*}
\n\t\ub97c \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc815\uc218 \\(d\\)\uac00 \uc788\ub2e4(\uc5ec\uae30\uc11c, \uc608\ub97c \ub4e4\uc5b4, \\(\\deg r(x)\\)\ub294 \\(r(x)\\)\uc758 \ucc28\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4).<\/p>\n

\t\uc774\uc81c \ubcf4\uc870\uc815\ub9ac 4\ub97c \uc774\uc6a9\ud558\uc5ec, \\(f(x),\\) \\(r_1(x),\\) \\(s_1(x)\\)\ub97c \uc801\ub2f9\ud55c \uc815\uc218 \\(c,\\) \\(c_1,\\) \\(c_2\\)\uc640 \uc801\ub2f9\ud55c \uc6d0\uc2dc\ub2e4\ud56d\uc2dd \\(g(x),\\) \\(r_2(x),\\) \\(s_2(x)\\)\ub97c \uc774\uc6a9\ud558\uc5ec
\n\\[f(x)=c\\cdot g(x),\\quad r_1(x)=c_1\\cdot r_2(x),\\quad s_1(x)=c_2\\cdot s_2(x) \\]
\n\ub85c \ub098\ud0c0\ub0b4\uc5c8\ub2e4\uace0 \ud558\uc790. \uc774\ub97c \uc774\uc6a9\ud574 \\(f(x)=r(x)s(x)\\)\ub97c \ub2e4\uc2dc \uc4f0\uba74
\n\\[
\ndc\\cdot g(x)=c_1c_2\\cdot r_2(x)s_2(x)
\n\\]
\n\uc778\ub370, \uc774\ub54c \uac00\uc6b0\uc2a4\uc758 \ubcf4\uc870\uc815\ub9ac\uc5d0 \uc758\ud574 \\(r_2(x)s_2(x)\\)\ub294 \uc6d0\uc2dc\ub2e4\ud56d\uc2dd\uc774\ub2e4. \ubcf4\uc870\uc815\ub9ac 4\uc758 \uc720\uc77c\uc131\uc5d0 \uc758\ud574 \\(dc\\)\uc640 \\(c_1c_2\\)\ub294 \ubd80\ud638\ub97c \ubb34\uc2dc\ud558\uba74 \ub3d9\uc77c\ud558\ub2e4. \ub530\ub77c\uc11c
\n\\[
\ndc\\cdot g(x)=udc\\cdot r_2(x)s_2(x),\\quad \\mbox{(\ub2e8, \\(u\\)\ub294 \\(1\\) \ud639\uc740 \\(-1\\)\uc774\ub2e4.)}
\n\\]
\n\uac00 \uc131\ub9bd\ud558\uba70 \uc774\ub294
\n\\[
\nf(x)=c\\cdot g(x)=(cu) r_2(x)s_2(x)
\n\\]
\n\uac00 \uc131\ub9bd\ud568\uc744 \ub73b\ud55c\ub2e4. \uc989 \\(f(x)\\)\uac00 \\(\\mathbb{Z}[x]\\)\uc758 (\\(f(x)\\)\ubcf4\ub2e4 \ucc28\uc218\uac00 \ub354 \ub0ae\uc740) \ub450 \ub2e4\ud56d\uc2dd\uc73c\ub85c \uc778\uc218\ubd84\ud574 \ub428\uc744 \ub73b\ud55c\ub2e4.\n<\/p>\n

\uc815\ub9ac 3\uc758 \ud544\uc694\uc870\uac74 \uc99d\uba85.<\/span><\/p>\n

\n\\(\\mathbb{Z}[x]\\subset \\mathbb{Q}[x]\\)\uc774\ubbc0\ub85c \uc790\uba85\ud558\ub2e4.
\n<\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\uac00\uc6b0\uc2a4\uc758 \ubcf4\uc870\uc815\ub9ac\uc5d0 \uad00\ud55c \uc9c8\ubb38\uc774 Share Your Math\uc5d0 \uc788\uc5b4\uc11c \uc774\uc5d0 \ub300\ud574 \uc18c\uac1c\ud558\uace0\uc790 \ud569\ub2c8\ub2e4. \u2018\uac00\uc6b0\uc2a4\uc758 \uc815\ub9ac\u2019\ub77c\uace0 \ub9d0\ud558\uba74 \uadf8 \uc885\ub958\uac00 \ub108\ubb34 \ub9ce\uc544\uc11c \ubb34\uc5c7\uc744 \uc77c\uceeb\ub294\uc9c0 \ud63c\ub3d9\uc758 \uc5ec\uc9c0\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uc9c0\uae08 \uc0b4\ud3b4\ubcf4\uace0\uc790 \ud558\ub294 \uac00\uc6b0\uc2a4\uc758 \ubcf4\uc870\uc815\ub9ac\ub294, \ubb3c\ub860, \uc9c8\ubb38\uacfc \uad00\ub828\uc788\ub294 \ub2e4\ud56d\uc2dd\uc758 \uc778\uc218\ubd84\ud574\uc640 \uad00\ub828\ub41c \uc815\ub9ac\uc785\ub2c8\ub2e4. \ub2ec\ube5b\ud559\uc0ac Share Your Math \uac8c\uc2dc\ud310\uc5d0 \uc62c\ub77c\uc628 \uc9c8\ubb38\uc758 \uc694\uc9c0\ub294 \uc815\uc218\uacc4\uc218 \ub2e4\ud56d\uc2dd\uc774 (\ucc28\uc218\uac00 \ub354 \ub0ae\uc740) \uc720\ub9ac\uacc4\uc218 \ub2e4\ud56d\uc2dd \ub450 \uac1c\ub85c \uc778\uc218\ubd84\ud574\ub420 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc774 \uadf8 \ub2e4\ud56d\uc2dd\uc774 (\ucc28\uc218\uac00 \ub354 \ub0ae\uc740) \uc815\uc218\uacc4\uc218 \ub2e4\ud56d\uc2dd \ub450 \uac1c\ub85c…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[59,54],"tags":[390,391,392,375],"class_list":["post-4715","post","type-post","status-publish","format-standard","hentry","category-abstract-algebra","category-basic-mathematics","tag-gausss-lemma","tag-ufd","tag-392","tag-375"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4715","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=4715"}],"version-history":[{"count":36,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4715\/revisions"}],"predecessor-version":[{"id":6132,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4715\/revisions\/6132"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=4715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=4715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=4715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}