044-pentagon-numbers.ipynb

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    "# Pentagon numbers\n",
    "## Problem 44 \n",
    "\n",
    "<div class=\"problem_content\" role=\"problem\">\n",
    "<p>Pentagonal numbers are generated by the formula, P<sub><var>n</var></sub>=<var>n</var>(3<var>n</var>&#8722;1)/2. The first ten pentagonal numbers are:</p>\n",
    "<p style=\"text-align:center;\">1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...</p>\n",
    "<p>It can be seen that P<sub>4</sub> + P<sub>7</sub> = 22 + 70 = 92 = P<sub>8</sub>. However, their difference, 70 &#8722; 22 = 48, is not pentagonal.</p>\n",
    "<p>Find the pair of pentagonal numbers, P<sub><var>j</var></sub> and P<sub><var>k</var></sub>, for which their sum and difference are pentagonal and D = |P<sub><var>k</var></sub> &#8722; P<sub><var>j</var></sub>| is minimised; what is the value of D?</p>\n",
    "</div>"
   ]
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   "execution_count": null,
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   "source": [
    "def solve():\n",
    "    # Your code here\n",
    "    \n"
   ]
  },
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   "source": [
    "## Solution"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "solve()"
   ]
  }
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