数学の問題の解答が一つだけしかないか確認

math_problem.ipynb

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    "## 問題\n",
    "ある自然数$x$がある．自然数$x$は$n,n+1(n\\leq200,n+1\\leq200)$を除く200以下の全ての自然数で割り切れるという性質を持つ．\n",
    "$n$,$n+1$の組をひとつ求めよ．\n",
    "\n",
    "## 回答\n",
    "1から200までの数の最小公倍数は，素因数分解すると奇数$k$を用いて$2^{7}k$という数字となる．ここで1から200までの数の最小公倍数を2と素数127で割った値を$y$とすると，$y$は127と128で割れない値になる．200以下の自然数に127以外に127の倍数はない．また$2^7$を素因数に持つ整数もない．よって$y$条件を満たす自然数$x$の条件を満たしている．よって$n,n+1$の組として(127,128)がある．\n",
    "\n"
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     "text": [
      "succ: N=50,ans1=31,ans2=32,x=49984588778161237200\n",
      "failed: N=100\n",
      "succ: N=150,ans1=127,ans2=128,x=19541714063639443819857654528657219411089303003820795960456000\n",
      "succ: N=200,ans1=127,ans2=128,x=1327927515090260884407345538562367745796828278681721394601759928808007945120777126248000\n",
      "succ: N=250,ans1=127,ans2=128,x=130772114744924574706363590925874340043529225687091412695324636034906746054600753955764866241169244952000\n",
      "succ: N=300,ans1=256,ans2=257,x=17538359604668456465621738470710851838830797427977636846629028507364462353333899882243878603401973940799038401578085611825296000\n",
      "succ: N=350,ans1=256,ans2=257,x=15710940042837302532926587682318922297070523871850343852586835880017268131333200637890980421517484774745187218555684944617703292807701121816827184000\n",
      "succ: N=400,ans1=256,ans2=257,x=116085483413080851997297607751181984039505286682906734766771141886928415432271142595094870432957320402858350965325934882166692109947052808387473745418094345294247430032000\n",
      "succ: N=450,ans1=256,ans2=257,x=54729498379647217035756720098255511324480611519572358326125124530649666892630329064131208366027803043859696791877198220452470709974955328618693674871716693196945016675937982263864677908586448000\n",
      "succ: N=500,ans1=256,ans2=257,x=142489537585511374696233218908642604727162136675660037055154066215167913270046135008419766186559001916864421413712857734850805473372808048821619534365096893681053337667228401393490062686262540049514002346573676112000\n",
      "failed: N=550\n",
      "failed: N=600\n",
      "failed: N=650\n",
      "failed: N=700\n",
      "failed: N=750\n",
      "failed: N=800\n",
      "failed: N=850\n",
      "failed: N=900\n",
      "failed: N=950\n",
      "failed: N=1000\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "def gcd(a,b):\n",
    "    if a>b:\n",
    "        return gcd(b,a)\n",
    "    else:\n",
    "        modula = b%a\n",
    "        if modula == 0:\n",
    "            return a\n",
    "        else:\n",
    "            return gcd(modula,a)\n",
    "\n",
    "def calc(N=200):\n",
    "    flag = True\n",
    "    \n",
    "    for i in range(1,N+1):\n",
    "        ans1 = i\n",
    "        ans2 = i+1\n",
    "        x = 1\n",
    "        \n",
    "        for j in range(1,N+1):\n",
    "            if j == ans1 or j == ans2:\n",
    "                pass\n",
    "            else:\n",
    "                a = gcd(x,j)\n",
    "                x = x * j // a\n",
    "        \n",
    "        if x % ans1 == 0 or x % ans2 == 0:\n",
    "            pass\n",
    "        else:\n",
    "            flag=False\n",
    "            print(\"succ: N=%d,ans1=%d,ans2=%d,x=%d\" %(N,ans1,ans2,x))\n",
    "    if flag:\n",
    "        print(\"failed: N=%d\" % N)\n",
    "\n",
    "for i in range(1,21):\n",
    "    calc(i*50)"
   ]
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