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    "#  Problem 6:\n",
    "\n",
    "[Euler Project #6](https://projecteuler.net/problem=6)\n",
    "\n",
    "> *The sum of the squares of the first ten natural numbers is,\n",
    "1^2+2^2+...+10^2=385\n",
    "\n",
    ">The square of the sum of the first ten natural numbers is,\n",
    "(1+2+...+10)^2=55^2=3025\n",
    "\n",
    ">Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025−385=2640.\n",
    "\n",
    ">Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.*\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reserved Space For Imports\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pprint\n",
    "import time  # Typically imported for sleep function, to slow down execution in terminal.\n",
    "import typing\n",
    "import decorators  # Typically imported to compute execution duration of functions.\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reserved Space For Method Definition\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(i: int,j: int):\n",
    "    '''\n",
    "    Function that computes the sum of a series of squared integers.\n",
    "    '''\n",
    "    series = [k**2 for k in range(i,j+1)]\n",
    "    #pprint.pprint(series)\n",
    "    summ = sum(series)\n",
    "    return summ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def square_of_sum(m: int,n: int):\n",
    "    '''\n",
    "    Function that computes the square of a summation of a series of integers.\n",
    "    '''\n",
    "    series = [p for p in range(m,n+1)]\n",
    "    summ = sum(series)**2\n",
    "    #print(summ)\n",
    "    return summ"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "## 1. Begin with testing the problem statement's example case.\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Mathematically, the trick is to recognize that this a LCM (Least Common Multiple) problem. The solution is list all the prime factors of each number in the factor list, then compute their collective product.*\n",
    "\n",
    " - [ ] Create a method that performs the first computation.\n",
    " - [ ] Create a method that performs the second computation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25164150\n"
     ]
    }
   ],
   "source": [
    "# Receive problem inputs...\n",
    "smallest_factor = 1\n",
    "largest_factor = 100\n",
    "\n",
    "a = square_of_sum(smallest_factor,largest_factor) - sum_of_squares(smallest_factor,largest_factor)\n",
    "print(a)\n"
   ]
  },
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   "execution_count": null,
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   "outputs": [],
   "source": []
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   "execution_count": null,
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   "cell_type": "code",
   "execution_count": null,
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