{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cvičení 1 s pomocí Maximy (25. 10. 2023)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 1\n",
    "\n",
    "Určete zbytek po dělení čísla $142$ číslem $6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{1}$}4\\]"
      ],
      "text/plain": [
       "(%o1)                                  4"
      ],
      "text/x-maxima": [
       "4"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod(142,6);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 2\n",
    "\n",
    "Určete zbytek po dělení čísla $122+171$ číslem 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{2}$}5\\]"
      ],
      "text/plain": [
       "(%o2)                                  5"
      ],
      "text/x-maxima": [
       "5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod(122+171,8);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 3\n",
    "\n",
    "Určete zbytek po dělení čísla $2^{30}$ číslem $15$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{3}$}4\\]"
      ],
      "text/plain": [
       "(%o3)                                  4"
      ],
      "text/x-maxima": [
       "4"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod(2^30,5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 4\n",
    "\n",
    "Určete zbytek po dělení čísla $181\\cdot 3^{70}$ číslem 13."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{4}$}10\\]"
      ],
      "text/plain": [
       "(%o4)                                 10"
      ],
      "text/x-maxima": [
       "10"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod(181*3^70,13);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 5\n",
    "\n",
    "Dokažte, že číslo $23^{25}+25^{23}$ je dělitelné číslem $48$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{5}$}0\\]"
      ],
      "text/plain": [
       "(%o5)                                  0"
      ],
      "text/x-maxima": [
       "0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod(23^25+25^23,48);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 6\n",
    "\n",
    "Dokažte první dvě vlastnosti Věty 1.1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 7\n",
    "\n",
    "Dokažte, že číslo  $2^{70}+3^{70}$ je dělitelné číslem $13$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{6}$}0\\]"
      ],
      "text/plain": [
       "(%o6)                                  0"
      ],
      "text/x-maxima": [
       "0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod(2^70+3^70,13);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Maxima",
   "language": "maxima",
   "name": "maxima"
  },
  "language_info": {
   "codemirror_mode": "maxima",
   "file_extension": ".mac",
   "mimetype": "text/x-maxima",
   "name": "maxima",
   "pygments_lexer": "maxima",
   "version": "branch_5_47_base_381_g45973baf2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}