52 lines
1.2 KiB
Markdown
52 lines
1.2 KiB
Markdown
---
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id: 5900f4711000cf542c50ff84
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title: 'Problem 261: Pivotal Square Sums'
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challengeType: 5
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forumTopicId: 301910
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dashedName: problem-261-pivotal-square-sums
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---
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# --description--
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Let us call a positive integer $k$ a square-pivot, if there is a pair of integers $m > 0$ and $n ≥ k$, such that the sum of the ($m + 1$) consecutive squares up to $k$ equals the sum of the $m$ consecutive squares from ($n + 1$) on:
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$${(k - m)}^2 + \ldots + k^2 = {(n + 1)}^2 + \ldots + {(n + m)}^2$$
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Some small square-pivots are
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$$\begin{align}
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& \mathbf{4}: 3^2 + \mathbf{4}^2 = 5^2 \\\\
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& \mathbf{21}: {20}^2 + \mathbf{21}^2 = {29}^2 \\\\
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& \mathbf{24}: {21}^2 + {22}^2 + {23}^2 + \mathbf{24}^2 = {25}^2 + {26}^2 + {27}^2 \\\\
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& \mathbf{110}: {108}^2 + {109}^2 + \mathbf{110}^2 = {133}^2 + {134}^2 \\\\
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\end{align}$$
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Find the sum of all distinct square-pivots $≤ {10}^{10}$.
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# --hints--
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`pivotalSquareSums()` should return `238890850232021`.
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```js
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assert.strictEqual(pivotalSquareSums(), 238890850232021);
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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 pivotalSquareSums() {
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return true;
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}
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pivotalSquareSums();
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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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