Project Euler Q45 - LO Man Hei

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    "### Q45\n",
    "It can be verified that \\(T_{285} = P_{165} = H_{143} = 40755\\).\n",
    "Find the next triangle number that is also pentagonal and hexagonal."
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    "def is_hexagonal(num):\n",
    "    k = int((2*num)**0.5) + 1\n",
    "    return True if k % 2 == 0 and (k//2)*(k-1) == num else False\n",
    "\n",
    "def is_triangle(num):\n",
    "    k = int((2*num)**0.5)\n",
    "    return True if k*(k+1)//2 == num else False\n",
    "\n",
    "def pentagonal_num(n):\n",
    "    return n*(3*n-1)//2\n",
    "\n",
    "def triangle_pentagonal_hexagonal_num(min_num):\n",
    "    i = 1\n",
    "    while True:\n",
    "        p_i = pentagonal_num(i)\n",
    "        if p_i > min_num and is_hexagonal(p_i) and is_triangle(p_i):\n",
    "            return p_i\n",
    "        i += 1"
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      "CPU times: user 12.8 ms, sys: 0 ns, total: 12.8 ms\n",
      "Wall time: 12.1 ms\n"
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       "1533776805"
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   "source": [
    "%%time\n",
    "triangle_pentagonal_hexagonal_num(40755)"
   ]
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    "def triangle_pentagonal_hexagonal_num_2(min_num):\n",
    "    i = 1\n",
    "    while True:\n",
    "        temp = (1+(48*i*i-24*i+1)**0.5)\n",
    "        if temp%6 == 0 and int((temp//6)*(temp//2-1)//2) > min_num:\n",
    "            return int((temp//6)*(temp//2-1)//2)            \n",
    "        i += 1"
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     "text": [
      "CPU times: user 4.13 ms, sys: 1.26 ms, total: 5.39 ms\n",
      "Wall time: 5.3 ms\n"
     ]
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       "1533776805"
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     "execution_count": 4,
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   "source": [
    "%%time\n",
    "triangle_pentagonal_hexagonal_num_2(40755)"
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