Intsqrt

intsqrt.ipynb

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      "n= 2354238731807548037258146419529716451839613714656910835753827857171\n",
      "n-sq**2 1439379138857298146653197327252975\n",
      "log10(diff),log10(sq) 33.15817520410052 33.18592525020733\n"
     ]
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   "source": [
    "import math\n",
    "\n",
    "def intsqrt(n):\n",
    "    sqnf=math.sqrt(n)\n",
    "    dig=math.ceil(math.log10(sqnf))\n",
    "    sq=0\n",
    "    for k in reversed(range(0,dig+1)):\n",
    "        for l in range(0,10):\n",
    "            sq+=10**k\n",
    "            if sq*sq==n:\n",
    "                break\n",
    "            if sq*sq>n:\n",
    "                sq-=10**k\n",
    "                break\n",
    "    return sq\n",
    "\n",
    "n=2354238731807548037258146419529716451839613714656910835753827857171\n",
    "sq=intsqrt(n)\n",
    "diff=n-sq*sq\n",
    "print('n=',n)\n",
    "print('n-sq**2',diff)\n",
    "print('log10(diff),log10(sq)',math.log10(diff),math.log10(sq))"
   ]
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Exact function which gives maximum integer m < sqrt(n) for given n.