modulus.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_powers(divisor, dividends = [10**i for i in range(1,23)]):\n",
    "    return [i % divisor for i in dividends]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4]\n",
      "[10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1]\n",
      "[10, 9, 12, 3, 4, 1, 10, 9, 12, 3, 4, 1, 10, 9, 12, 3, 4, 1, 10, 9, 12, 3]\n",
      "[10, 15, 14, 4, 6, 9, 5, 16, 7, 2, 3, 13, 11, 8, 12, 1, 10, 15, 14, 4, 6, 9]\n",
      "[10, 5, 12, 6, 3, 11, 15, 17, 18, 9, 14, 7, 13, 16, 8, 4, 2, 1, 10, 5, 12, 6]\n",
      "[10, 8, 11, 18, 19, 6, 14, 2, 20, 16, 22, 13, 15, 12, 5, 4, 17, 9, 21, 3, 7, 1]\n"
     ]
    }
   ],
   "source": [
    "for i in [2,3,5,7,11,13,17,19,23]:\n",
    "    print(check_powers(i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13\n",
      "26\n",
      "39\n",
      "52\n",
      "65\n",
      "78\n",
      "91\n",
      "104\n",
      "117\n",
      "130\n",
      "143\n",
      "156\n",
      "169\n",
      "182\n",
      "195\n",
      "208\n",
      "221\n",
      "234\n",
      "247\n",
      "260\n",
      "273\n",
      "286\n",
      "299\n",
      "312\n",
      "325\n",
      "338\n",
      "351\n",
      "364\n",
      "377\n",
      "390\n",
      "403\n",
      "416\n",
      "429\n",
      "442\n",
      "455\n",
      "468\n",
      "481\n",
      "494\n",
      "507\n",
      "520\n",
      "533\n",
      "546\n",
      "559\n",
      "572\n",
      "585\n",
      "598\n",
      "611\n",
      "624\n",
      "637\n",
      "650\n",
      "663\n",
      "676\n",
      "689\n",
      "702\n",
      "715\n",
      "728\n",
      "741\n",
      "754\n",
      "767\n",
      "780\n",
      "793\n",
      "806\n",
      "819\n",
      "832\n",
      "845\n",
      "858\n",
      "871\n",
      "884\n",
      "897\n",
      "910\n",
      "923\n",
      "936\n",
      "949\n",
      "962\n",
      "975\n",
      "988\n"
     ]
    }
   ],
   "source": [
    "for i in range(1,1000):\n",
    "    if i % 13 == 0:\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.000000082740371"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 10**-10\n",
    "(np.e**a-1)/a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.e**a)/(a+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.605170185988091"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(10**-14,10,10000)\n",
    "y = np.log(np.e**x -1) - np.log(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iHgr8wjl3HhALxDnnXjezXwU2mkhw2lFwgPFvLWP+qu0M7dKUpy7VsjsJrCMWtZndB9wHUDmivkslLZHqoxVbGT9rOfsOlPHQyJ5cOyRRy+4k4LSOWsQH+w6U8ei7K5m+cCM9W8cxaXRfurY87I9sRPzqqIrazD4DPgtIEpEgtShnN+OmL2XjniJuGdaZsSOSiInW8VhSczSiFjmMkrIKJs3/gRc+W0eb+Lq8qeOxxCMqapFqrN1ewNjpS8jYlM9lKe14cGRPGup4LPGIilqkiooKY/JX2TwxbxX160Tzj18N4JzerbyOJRFORS1SaePuIu6asZRvs3YzvHsLHr/kBFo0jPU6loiKWsTMmP79Rh6duxLnHE9c0odLU9rhnJbdSXBQUUtE255fzPhZy/lk1XZO6tSEJ0cl65BZCToqaolYc5Zu5sG3MyguLWfCBT25ZrBuXpHgpKKWiLO7sIQH38ngvWVbSG4fz8TLkuncvIHXsUQOS0UtEWV+5jbufWs5eftLuPvsbtx4aieio3TzigQ3FbVEhILiUh6du5I3F+bSvVVD/vUbnbwioUNFLWHvq3U7uXvGMrbk7eeWYZ0ZM6IrdaJ18oqEDhW1hK39JeX8Zd4qXv0qm47N6jPjpiEM6NDY61giR01FLWEpfcMe7npzKet3FnLN4A7ce2536sXoy11Ck75yJawcKCvnmflreOGzdbSKi2XK9YMYqvMLJcSpqCVsLM/N464ZS1m9rYBRA9rx0AU9idNGShIGVNQS8g6UlfPcJ2v5+2fraFo/hpevSeGMHi29jiXiNypqCWlVR9EX92/LhJG9aFRPo2gJL76cQh4LLADqVF4/08wmBDqYyM/RKFoiiS8j6gPAcDPb55yrDXzhnPvAzL4JcDaRamkULZHGl1PIDdhX+W7tyv8skKFEqqNRtEQqn+aonXNRwCKgC/C8mX1bzTWpQCpAQkKCPzOKaBQtEc2nojazcqCvcy4emO2c621mGYdckwakAaSkpGjELX6hUbTIUa76MLO9zrnPgHOAjCNcLnJcqo6iL+nfjodG9tQoWiKSL6s+mgOllSVdFxgB/CXgySRiVR1FN2sQwyvXpjC8u0bRErl8GVG3Bl6rnKeuBbxpZnMDG0si1dKNe7ln5jKNokWq8GXVxzKgXw1kkQi2v6SciR+v5uUvsmjRMFZz0SJV6M5E8dzX63YxftYycnYVceWgBMaf2117dIhUoaIWz+QXl/Ln91cx7bsNdGhaj6k3DGJIZ+10J3IoFbV4Yn7mNn4/O4PtBcWkntqJcSOSqBujU1dEqqOilhq1a98BHnl3JXOWbqZ7q4a8ePUAktvHex1LJKipqKVGmBlzlm7mkXdXUlBcyrgRSdw8rDMx0ToBXORIVNQScFvy9vPA7Azmr9pO3/bxPDGqD0ktG3odSyRkqKglYCoqjDe+38if38+ktKKCB87vwXVDOxJVy3kdTSSkqKglILJ3FjJ+1jK+Wb+bIZ2b8vjFfUhoWs/rWCIhSUUtflVaXkHagvU8M38NMVG1ePziE7h8YHuc0yha5FipqMVv0jfs4f5Zy1m1tYBze7fi4V/0omVcrNexREKeilqOW0FxKU9+uJp/f5NDq7hY/vnrFM7sqdu/RfxFRS3HZV7GVibMyWB7wQGuHZLInWd1o0EdfVmJ+JO+o+SYbMnbz4R3VvDRym30aB3Hi1en0Fc3rogEhIpajkp5hfH6Nzk8+eFqyioquO/c7vzm5I7UjtKNKyKBoqIWn2Vuyee+WctZsnEvp3Rtxp8uOkFL7kRqgIpajqi4tJxJ89fwzwXraVS3NpNG9+UXyW205E6khvhyFFd74F9AK6ACSDOzSYEOJsFhwQ87ePCdDHJ2FXHpgHbcf14PGteP8TqWSETxZURdBtxpZunOuYbAIufcx2a2MsDZxENb84p59L2VvLdsCx2b1dde0SIe8uUori3Alsq3C5xzmUBbQEUdhsrKK3jt6xwmfrSa0grjd2cmceNpnagTrb2iRbxyVHPUzrlEDp6f+G1A0oinFuXs4YG3M8jcks9pSc35w4W96NC0vtexRCKez0XtnGsAvAWMNbP8aj6fCqQCJCQk+C2gBN7eohL+Mm8V077bSKu4WF64qj/n9G6lHxaKBAmfito5V5uDJT3FzGZVd42ZpQFpACkpKea3hBIwFRXGzPRcHv9gFXn7S7nhlI6MGZGkOwtFgowvqz4c8DKQaWYTAx9JasLqrQU88PZyvs/ew4AOjfnjRb3p0TrO61giUg1fhk5DgauB5c65JZUfu9/M3g9YKgmYwgNlTJq/hpe/yCIuNponLunDqAHtqKXN/EWCli+rPr4A9F0c4syMeRlbeXTuSjbnFTN6YHvuPae71kSLhABNRkaANdsKePjdFXy5dhfdWzXk2Sv7MaBDE69jiYiPVNRhrKC4lGfmr2Hyl9nUi4nikV/04qpBCURrAyWRkKKiDkNmxuzFm/jzB6vYue8Al6e05+6zu9G0QR2vo4nIMVBRh5mMTXk8PGcFC3P2kNw+npd+nUKy9okWCWkq6jCxp7CEv368mqnfbqBxvRieGNWHUf21mkMkHKioQ1x5hfHG9xt48sPVFBSX8evBiYw7M4lGdWt7HU1E/ERFHcIW5exhwpwMMjblM6hjEx65sBfdW+mmFZFwo6IOQZv37ufxD1YxZ+lmWsXF8uwV/RjZp7X25hAJUyrqEFJUUsY//rOetAXrMIPbh3fhptM6U197c4iENX2Hh4CKCuPtJZv4y7xVbMs/wAXJbbj3nG60a6zzCkUigYo6yC3K2cMf5q5k6ca9JLdrxPNX9iclUXcVikQSFXWQqjoP3TKuDhMvS+aivm213E4kAqmog8yh89B3DO/CjZqHFolo+u4PEuUVB2/7fvLD/5+HHn9ud9rG1/U6moh4TEUdBD5fs4PH3l9F5pZ8kts14u9X9dfudiLyf1TUHlq5OZ8/f5DJ52t20r5JXZ65oh8jT2iteWgR+QkVtQe25O3nqQ9/YNbiXOJia/PA+T24enAH6kRHeR1NRIKQL2cmvgKMBLabWe/ARwpf+cWl/OOzdbz8RRYGpJ7SiVuGdaFRPe3LISKH58uI+lXgOeBfgY0SvkrKKpj6bQ7PfLKW3YUlXNS3DXedrRtWRMQ3vpyZuMA5l1gDWcKOmfFBxlaemLeK7F1FDOnclPvP60Hvto28jiYiIcRvc9TOuVQgFSAhIcFfDxuSzIwv1u7kyQ9Xsyw3j24tGzL5uoEMS2qujZNE5Kj5rajNLA1IA0hJSTF/PW6oSd+whyfnrebr9btoG1+XJ0f14eL+7YjSSg4ROUZa9eEnq7cW8NRHq/l45TaaNYjh4Qt6csWgBK3kEJHjpqI+Tht3F/G3j39g9pJNNIiJ5q6zkrhuaEfd8i0ifuPL8rxpwDCgmXMuF5hgZi8HOliw215QzHOfrGXadxuo5Rypp3biplM707h+jNfRRCTM+LLq44qaCBIq9hSW8M/P1zP5y2xKyyu4fGB77jijKy3jYr2OJiJhSv8+99HeohJe+jyLV7/KprCkjAv6tOF3ZyaR2Ky+19FEJMypqI8gb38pL3+RxeQvsig4UMb5J7RmzIiuJLVs6HU0EYkQKurDyC8u5ZUvsnj5iywKiss4t3crxozoqlO+RaTGqagPUVBcyuQvs3np8/XkF5dxVs+WjB2RRM82KmgR8YaKutK+A2W89lU2aQvWk7e/lBE9WjJ2RFfd7i0inov4ot5bVMLkL7N59ats8vaXckb3FowdkcQJ7VTQIhIcIraotxcU8/LnWbz+TQ6FJeWc2bMlt53eheT28V5HExH5iYgr6k1795P2n3W88f1GSssrGNmnDbec3lk/JBSRoBUxRZ21s5AXPlvLrPRNAFzcvy03D+tCR62DFpEgF/ZFvXprAc9/upa5yzZTO6oWVw1KIPW0zjrdW0RCRlgWtZnxzfrdpC1Yx6erd1A/JoobTunEb0/pSIuGutVbREJLWBV1eYUxL2MraQvWsTQ3j6b1Yxg3IolrhnQgvp42SxKR0BQWRb2/pJwZizby0udZbNhdRGLTevzxot6MGtCO2NraD1pEQltIF/WufQd47esc/v11NnuKSunbPp77z+vOmT1b6UQVEQkbIVnUWTsLefmL9cxYmMuBsgpG9GhB6qmdGZjYWGcSikjYCZmi/vHA2MlfZvPJqu3ERNXion5tSD21E11aaCc7EQlfQV/U+0vKmbU4l1e/zGbN9n00axDDmDO6ctVJCVrBISIRwaeids6dA0wCooCXzOzxgKYCNu/dz7++zuGN7zewt6iUXm3ieOrSZC5Ibq0DY0UkovhyZmIU8DxwJpALfO+cm2NmK/0dxsxYlLOHyV9mM2/FVsyMs3u14rqhHTX/LCIRy5cR9YnAWjNbD+CcewO4EPBrUecXl3LtK9+RvmEvcbHRXH9yR64e3IF2jev582lEREKOL0XdFthY5f1cYNChFznnUoFUgISEhKMO0rBONAlN6vHLfm25ZEA76sUE/fS5iEiN8KUNq5tvsP/6gFkakAaQkpLyX58/4pM4x9Oj+x3tbxMRCXu1fLgmF2hf5f12wObAxBERkUP5UtTfA12dcx2dczHAaGBOYGOJiMiPjjj1YWZlzrnbgA85uDzvFTNbEfBkIiIC+LiO2szeB94PcBYREamGL1MfIiLiIRW1iEiQU1GLiAQ5FbWISJBzZkd9b8qRH9S5HUDOMf72ZsBOP8YJBXrN4S/SXi/oNR+tDmbWvLpPBKSoj4dzbqGZpXidoybpNYe/SHu9oNfsT5r6EBEJcipqEZEgF4xFneZ1AA/oNYe/SHu9oNfsN0E3Ry0iIj8VjCNqERGpQkUtIhLkgqaonXPnOOdWO+fWOufGe50n0Jxz7Z1znzrnMp1zK5xzY7zOVFOcc1HOucXOubleZ6kJzrl459xM59yqyj/vwV5nCjTn3LjKr+sM59w051ys15n8zTn3inNuu3Muo8rHmjjnPnbOran8tbE/nisoirrKAbrnAj2BK5xzPb1NFXBlwJ1m1gM4Cbg1Al7zj8YAmV6HqEGTgHlm1h1IJsxfu3OuLXAHkGJmvTm4PfJob1MFxKvAOYd8bDww38y6AvMr3z9uQVHUVDlA18xKgB8P0A1bZrbFzNIr3y7g4DdvW29TBZ5zrh1wPvCS11lqgnMuDjgVeBnAzErMbK+noWpGNFDXORcN1CMMT4UyswXA7kM+fCHwWuXbrwEX+eO5gqWoqztAN+xL60fOuUSgH/Ctx1FqwtPAPUCFxzlqSidgBzC5crrnJedcfa9DBZKZbQKeAjYAW4A8M/vI21Q1pqWZbYGDgzGghT8eNFiK2qcDdMORc64B8BYw1szyvc4TSM65kcB2M1vkdZYaFA30B14ws35AIX7653CwqpyXvRDoCLQB6jvnfuVtqtAWLEUdkQfoOudqc7Ckp5jZLK/z1IChwC+cc9kcnN4a7px73dtIAZcL5JrZj/9amsnB4g5nI4AsM9thZqXALGCIx5lqyjbnXGuAyl+3++NBg6WoI+4AXeec4+C8ZaaZTfQ6T00ws/vMrJ2ZJXLwz/gTMwvrkZaZbQU2Oue6VX7oDGClh5FqwgbgJOdcvcqv8zMI8x+gVjEHuKby7WuAd/zxoD6dmRhoEXqA7lDgamC5c25J5cfurzyfUsLL7cCUykHIeuA6j/MElJl965ybCaRzcHXTYsLwdnLn3DRgGNDMOZcLTAAeB950zv2Wg39hXeqX59It5CIiwS1Ypj5EROQwVNQiIkFORS0iEuRU1CIiQU5FLSIS5FTUIiJBTkUtIhLk/he8k0sPZpyddgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7.99597430e-04,  5.00091680e-04,  1.00026671e-03, ...,\n",
       "        7.69556926e+00,  7.69646938e+00,  7.69736951e+00])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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