{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0e2b0144-f195-451c-b92b-4cc61db0e500",
   "metadata": {},
   "source": [
    "# Vollkommene Zahlen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1423c68-49a6-4f33-a8f3-db30ddccc543",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "<b>Ziel des Notebooks:</b>\n",
    "    \n",
    "- Mersenne-Primzahlen\n",
    "- vollkommene Zahlen    \n",
    "- befreundete Zahlen\n",
    " \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23be4734-b454-42c7-9252-fb0acbce9020",
   "metadata": {},
   "source": [
    "Bevor wir uns mit vollkommenen Zahlen, ihrer Bedeutung in der Mythologie und ein paar spannenden Eigenschaften beschäftigen können, müssen wir den Begriff der Teilersumme kennenlernen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d819ae8-a5b5-47f4-9d79-785596ceff76",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    " \n",
    "Die <b>Teilersumme</b> einer Zahl ist definiert als die Summe ihrer Teiler, bei welchen insbesondere auch die Zahl selbst eingeschlossen ist. \n",
    "\n",
    "Wenn man die Zahl selbst in der Summe ausschließen möchte, nennt man sie die Teilersumme aller echten Teiler. Im Rahmen dieses Notebooks nennen wir sie die echte Teilersumme.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb9aa8a2-a945-48a3-95e5-ecc82e51e737",
   "metadata": {},
   "source": [
    "Eine Zahl kann nun in verschiedenen Verhältnissen zu ihrer echten Teilersumme stehen. Wenn die echte Teilersumme größer als die Zahl selbst ist, nennt man sie <b>abundant</b>, wenn die echte Teilersumme kleiner ist, nennt man sie <b>defizient</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67b1135c-4060-4a51-9bff-457476f6255f",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    " \n",
    "Wenn eine natürliche Zahl gleich ihrer echten Teilersumme ist, wird sie <b>vollkommene Zahl</b> genannt.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b29039d-7f00-4ace-aba7-97422c068b4a",
   "metadata": {},
   "source": [
    "Anicius Manlius Severinus Boethius, ein Philosoph des 5. und 6. Jahrhunderts n. Chr., lies sich in seiner Zahlenlehre nicht nur auf Zahlen als mathematische Objekte beschränken, sondern betrachtete sie auch von einem ethischen Standpunkt. Schon die Namen dieser drei Typen von Zahlen, lassen darauf schließen, dass man vollkommene Zahlen als wertvoller und besser erachtete als die anderen Zahlen. Während vollkommene Zahlen Ordnung und Tugend verkörpern, vergleicht er abundante Zahlen mit dreiköpfigen Geryonen und defizitäre Zahlen mit einäugigen Zyklopen, also Lebewesen, welche die Mitte zwischen Überfluss und Mangel nicht finden konnten."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f05def07-c66d-45a2-a802-2f3155fee0a0",
   "metadata": {},
   "source": [
    "Beispiele:\n",
    "\n",
    "Die erste vollkommene Zahl ist die 6. Ihre echten Teiler sind 1,2 und 3, deren Summe leicht zu erkennen gleich 6 ergibt.\n",
    "\n",
    "Die nächste vollkommene Zahl ist auch noch überschaubar groß: 28 = 1 + 2 + 4 + 7 + 14. Danach folgen 496, 8128 und 33.550.336.\n",
    "\n",
    "Die ersten 10 natürlichen Zahlen - ausgenommen der 6 - sind defizient. 12, 20 und 24 sind abundant.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9599a8d-3836-4175-ba13-2aa896f2d39d",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe \n",
    "***\n",
    "    \n",
    "Beweisen Sie:  \n",
    "1. Es gibt unendlich viele abundante Zahlen.\n",
    "2. Es gibt unendlich viele defiziente Zahlen.\n",
    "    \n",
    "<i>Hinweis:</i> Untersuchen Sie den Zusammenhang von Primzahlen mit defizienten und abundanten Zahlen.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e75c4736-1268-40a6-a8f5-4263dfc4a5e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "###LÖSUNG AUFGABE \n",
    "\n",
    "\n",
    "\n",
    "###ENDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1133a9c1-75e9-4836-837f-3cf0b19e549f",
   "metadata": {},
   "source": [
    "(Un)nützes Wissen:\n",
    "\n",
    "Alle 17 Jahre werden Teile Afrikas von einer Zikadenplage überfallen. Jene Zikaden leben nach dem Schlüpfen für den gesamten Zeitraum als Larven unter der Erde und kommen dann auf die Woche genau nach 17 Jahren heraus. Dieser zunächst eigenartige Lebenszyklus ist eine gut gewählte Überlebensstrategie. Das massenhafte Auftreten soll dabei helfen die Fressfeinde zu übersättigen und das Überleben von zumindest einigen Zikaden sicherzustellen. Die doch ziemlich große Primzahl hat wahrscheinlich den Hintergrund, Überschneidungen mit den Lebenszyklen anderer Fressfeinde gering zu halten. So müssen sich die Zikaden jedes Jahr nur mit denjenigen herumschlagen, die jedes Jahr jagen oder auch genau alle 17 Jahre, im selben Zyklus. \n",
    "\n",
    "Die Theorie jenen Fressfeinden auszuweichen ist aber insofern umstritten, als dass noch kein solcher Fressfeind gefunden wurde."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a9c29b9-41c3-4e54-bfa5-68ad1615e535",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Recherche-Aufgabe \n",
    "***\n",
    "    \n",
    "Finden Sie weitere Beispiele, bei denen Primzahlen oder andere besondere Zahlen eine Rolle in Natur, Kultur oder Mythologie spielen.  \n",
    "    \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d0d80cc3-44fb-41f8-afe7-0e20af4b2f07",
   "metadata": {},
   "outputs": [],
   "source": [
    "###LÖSUNG AUFGABE \n",
    "\n",
    "\n",
    "\n",
    "###ENDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "381a3e56-d38e-43bb-9833-d5d88c12618c",
   "metadata": {},
   "source": [
    "Ein besonderer Typ Primzahl, der für das Finden vollkommener Zahlen eine Bedeutung hat, ist eine Mersenne-Primzahl."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18ea4ded-c402-48c5-815f-40e4773f91f6",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    " \n",
    "Sei n eine natürliche Zahl. Falls $2^n -1$ eine Primzahl ist, wird sie <b>Mersenne-Primzahl</b> genannt.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0ae2e9-3246-4e3f-bbd6-2dd6da6fe746",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe \n",
    "***\n",
    "    \n",
    "Überprüfen Sie für einige Zahlen der Folge $(2^n-1)_{n \\in \\mathbb{N}}$, ob sie Mersenne-Primzahlen sind.    \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "65e3967c-c730-4246-9612-ddc94745eac8",
   "metadata": {},
   "outputs": [],
   "source": [
    "###LÖSUNG AUFGABE \n",
    "\n",
    "\n",
    "\n",
    "###ENDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f817858f-733a-4a7b-b4fb-732e386877d0",
   "metadata": {},
   "source": [
    "Es ist weder bekannt, ob es unendlich viele Mersenne-Primzahlen gibt, noch ob es unendlich viele nicht-Primzahlen der Form $2^n-1$ gibt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21fbab0e-d837-46c6-8cdb-21ac8fe2627d",
   "metadata": {},
   "source": [
    "### Eigenschaften vollkommener Zahlen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "371a3dbd-ea72-454c-b89b-29382b06dc2d",
   "metadata": {},
   "source": [
    "Die Frage, ob es unendlich viele vollkommene Zahlen gibt, ist unmittelbar daran geknüpft, ob es unendlich viele Mersenne-Primzahlen gibt. Dies zeigt der nachfolgende Satz."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a85d9c8c-1547-4f14-a91c-f1c83c68fca9",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "<b>Satz von Euklid und Euler:</b>\n",
    "    \n",
    "$2^{k-1}*(2^k-1)$ ist genau dann eine vollkommene Zahl, wenn $2^k-1$ eine Mersenne-Primzahl ist.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "648d7f22-9790-4d61-90ea-3e363f3c9c66",
   "metadata": {},
   "source": [
    "Der Beweis beruht auf der Annahme, dass für zwei Teilerfremde natürliche Zahlen, die (nicht echte) Teilersumme des Produkts gleich des Produkts der einzelnen Teilersummen ist. \n",
    "\n",
    "Sei $\\sigma(x)$ die Funktion, die einer Zahl ihre Teilersumme zuordnet, dann kann man die obige Aussage auch so formulieren:\n",
    "\n",
    "<b>$\\sigma(a*b) = \\sigma(a)*\\sigma(b)$ für a,b teilerfremd</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "806bd56a-479b-41fd-9574-57a348882cd2",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "Denkanstoß: Beweisen sie diese Aussage.    \n",
    "<div/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c14dd9d3-629d-4031-be33-5898b78c6a53",
   "metadata": {},
   "source": [
    "<i>Beweis:</i>\n",
    "\n",
    "Sei also $n = 2^{k-1} * (2^k-1)$, wobei $2^k-1$ prim ist.\n",
    "\n",
    "n hat genau $2k-1 $ verschiedene echte Teiler von der Art: \n",
    "\n",
    "$2^i$, mit i = 0, 1, .., k-1 bzw. $2^i * (2^k-1)$, mit i = 0, 1, ..., k-2 sind.\n",
    "\n",
    "Um zu beweisen, dass eine solche Zahl vollkommen ist, betrachten wir also ihre echte Teilersumme:\n",
    "\n",
    "$ \\sum\\limits_{i=0}^{k-1} 2^i + (2^k-1)* \\sum\\limits_{i=0}^{k-2}2^i = 2^k - 1 + (2^{k-1} - 1) = (2^k - 1)*2^{k-1} = n $. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffd11180-5944-4385-9d77-50bc1a8ef323",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "Denkanstoß: Vollziehen Sie die einzelnen Schritte nach.    \n",
    "<div/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb6b2d2a-fb1c-4d2a-9a83-55d229962a32",
   "metadata": {},
   "source": [
    "Alle bisher gefundenden vollkommenen Zahlen sind gerade. Es ist nicht bekannt, ob es auch ungerade vollkommene Zahlen gibt, eine solche Zahl müsste aber größer als $10^{1500}$ sein! Beschäftigen wir uns also erst einmal mit den Eigenschaften von geraden volkommenen Zahlen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "595f945f-974f-4d2e-ae80-d4d1f8861219",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe \n",
    "***\n",
    "Beweisen Sie:\n",
    "    \n",
    "1. Jede gerade vollkommene Zahl endet entweder auf 6 oder auf 8. \n",
    "2. Die Summe der Kehrwerte aller Teiler einer vollkommenen Zahl ergibt 2.\n",
    "    \n",
    "<i>Hinweis:</i> In den Teilern ist auch die Zahl selbst eingeschlossen.\n",
    "<div/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a5d10210-9426-4f0b-9bb5-2c2a95c9f535",
   "metadata": {},
   "outputs": [],
   "source": [
    "###LÖSUNG AUFGABE \n",
    "\n",
    "\n",
    "\n",
    "###ENDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bc84662-3dc8-4611-866d-69fbf3b84617",
   "metadata": {},
   "source": [
    "(Un)nützes Wissen:\n",
    "\n",
    "Wer sich jetzt bei all diesen Definitionen fragt, wer sich da die Namen ausgedacht hat, es gibt auch sogenannte \"merkwürdige Zahlen\". Das sind Zahlen, deren echte Teilersumme größer als sie selbst ist und die sich nicht als Summe einer Teilmenge ihrer echten Teiler schreiben lässt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c053836-d417-49f3-b102-109ae6dc3f07",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Befreundete Zahlen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1820e386-9572-45c1-acef-f74f4032147e",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "<i> Auf die Frage was ein Freund sei, antwortete er: \"Einer der ein anderes Ich ist, wie 220 und 284.\" - </i>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c68f000-bb09-4b80-8b07-f074eaf5210a",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    " \n",
    "<b>Befreundete Zahlen</b> zeichnen sich dadurch aus, dass die echte Teilersumme der einen Zahl gleich der echten Teilersumme der anderen Zahl ist.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3045ed5a-7a68-426f-bab1-0013f87effab",
   "metadata": {},
   "source": [
    "Die Teiler von 220 sind: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 und 110. \n",
    "Die Teiler von 284 sind: 1, 2, 4, 71 und 142 \n",
    "\n",
    "Es lässt sich nun leicht nachrechnen, dass: 1+2+4+5+10+11+20+22+44+55+110=284 und 1+2+4+71+142 = 220"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a84ffd6-6b27-4c01-ae2e-c9a5e9df59a6",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Satz von Thabit:</b>\n",
    "    \n",
    "Seien n, x, y und z natürliche Zahlen, wobei:\n",
    "    \n",
    "    \n",
    "$x = 3 * 2^n - 1 , $  \n",
    "$y = 3 * 2^{n-1} -1 $ und  \n",
    "$z = 9 * 2^{2*(n-1)} - 1 $\n",
    "    \n",
    "Falls x, y und z größer als zwei sind, sind $a = 2^n*x*y$ und $b = 2^n*z$ befreundet.\n",
    "     \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a81d481-0d35-4799-a4ee-083c30c3919b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe \n",
    "***\n",
    "    \n",
    "1. Geben Sie den Beweis des Satzes von Thabit wieder.\n",
    "2. Angelehnt an seinen Satz nennt man Zahlen der Form $x = 3 * 2^n - 1$ Thabit-Zahlen.\n",
    "Beweisen Sie, dass zwei aufeinanderfolgende Thabit-Zahlen prim sind.  \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "975cf408-004c-4136-a5ab-1d4758ae0fb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "###LÖSUNG AUFGABE \n",
    "\n",
    "\n",
    "\n",
    "###ENDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe77049c-fdce-4f68-a335-b9b43d96a183",
   "metadata": {},
   "source": [
    "Wenn man mit mehr als zwei natürlichen Zahlen einen Zyklus über die Teilersumme bilden kann, nennt man diese Gruppe <b>gesellige Zahlen.</b>"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "f81bab66-05c4-410f-83a0-c28fb0a19834",
   "metadata": {},
   "source": [
    "\n",
    "<div>\n",
    "<img src=\"attachment:71062bc6-f5ba-466d-bd30-09fea39a5544.png\" width=\"250\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5011294-0063-4f9d-b9d1-423d5d2fb222",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Recherche-Aufgabe \n",
    "***\n",
    "    \n",
    "Finden Sie weitere Beispiele für gesellige Zahlen. Gibt es zu jeder Kettengröße eine Gruppe geselliger Zahlen?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7973bc20-4e48-4ad9-8b04-dcc34d307cca",
   "metadata": {},
   "outputs": [],
   "source": [
    "###LÖSUNG AUFGABE \n",
    "\n",
    "\n",
    "\n",
    "###ENDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd24fb4a-272f-4f94-b399-9fd2d9d9784b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "### Rückblick-Aufgabe\n",
    "***\n",
    "    \n",
    "Man nennt eine Zahl <b>quasiperfekt</b>, wenn ihre echte Teilersumme nur eins größer oder kleiner als sie ist.\n",
    "    \n",
    "Geben Sie Euklids Beweis wieder, dass es keine quasiperfekten Zahlen gibt, bei denen die echte Teilersumme größer als die Zahl selbst ist.\n",
    "    \n",
    "Finden Sie noch mehr interessante Beobachtungen bezüglich der Teilersumme einer Zahl?\n",
    "      \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d3b90b4-e101-44ea-8f63-207043419eda",
   "metadata": {},
   "source": [
    "Quellen:\n",
    "\n",
    "https://www.spektrum.de/news/im-zikadenleben-zaehlen-zahlen/591101\n",
    "\n",
    "https://de.wikipedia.org/wiki/Befreundete_Zahlen\n",
    "\n",
    "https://de.wikipedia.org/wiki/Mersenne-Zahl\n",
    "\n",
    "https://de.wikipedia.org/wiki/Vollkommene_Zahl\n",
    "\n",
    "https://de.wikipedia.org/wiki/Abundante_Zahl\n",
    "\n",
    "https://de.wikipedia.org/wiki/Boethius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab7fdd21-a672-4888-94f5-87500bb9058f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}