// Numbas version: exam_results_page_options {"name": "Abbildungen (Goldbach-Vermutung)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Abbildungen (Goldbach-Vermutung)", "tags": [], "metadata": {"description": "

Questions around the notion of map, with underlying topic the statement of Goldbach's conjecture. The student has to write the conjecture (by filling in some gaps) as a surjectivity statement for a map, and compute some preimages of elements.

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(In German)

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Eine weitere Übung zum Umgang mit dem Abbildungsbegriff.

b)

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c)

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d)

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Eine mögliche Antwort ist $\\simplify{{result_d}}$:

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;\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Die Goldbachsche Vermutung (aufgestellt 1742 von Christian Goldbach in einem Brief an Euler und bis heute offen) sagt aus, dass sich jede gerade Zahl, die größer ist als $2$, als die Summe von zwei Primzahlen schreiben lässt. Füllen Sie die Lücken in dem folgenden Text aus:

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Eine äquivalente Formulierung der Goldbach-Vermutung ist gegeben durch:

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Sei $\\mathbb P$ die Menge aller [[0]].

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Dann ist die Abbildung

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$G\\colon\\mathbb P \\times \\mathbb P \\to \\{ n\\in \\mathbb Z;\\ n$ ist [[1]] und [[2]] $2\\}$,

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$(x, y) \\mapsto$ [[3]],

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[[4]].

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$G($ [[0]], [[1]] $) = \\var{a2}$.

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(Es gibt in der Regel mehrere richtige Antworten. Wenn Sie \"Antworten aufdecken\" wählen, werden unten bei den Hinweisen alle möglichen Antworten angezeigt.)

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