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45 lines
931 B
Markdown
45 lines
931 B
Markdown
---
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id: 5900f3f31000cf542c50ff06
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title: 'Problem 135: Gleiche Unterschiede'
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challengeType: 1
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forumTopicId: 301763
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dashedName: problem-135-same-differences
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---
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# --description--
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Given the positive integers, $x$, $y$, and $z$, are consecutive terms of an arithmetic progression, the least value of the positive integer, $n$, for which the equation, $x^2 − y^2 − z^2 = n$, has exactly two solutions is $n = 27$:
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$$34^2 − 27^2 − 20^2 = 12^2 − 9^2 − 6^2 = 27$$
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Es stellt sich heraus, dass $n = 1155$ der kleinste Wert ist, der genau zehn Lösungen hat.
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Wie viele Werte von $n$, unter einer Million, haben genau zehn verschiedene Lösungen?
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# --hints--
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`sameDifferences()` sollte `4989` zurückgeben.
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```js
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assert.strictEqual(sameDifferences(), 4989);
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```
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# --seed--
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## --seed-contents--
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```js
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function sameDifferences() {
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return true;
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}
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sameDifferences();
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```
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# --solutions--
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```js
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// solution required
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```
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