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---
id: 5900f4711000cf542c50ff84
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title: 'Problem 261: Somme di quadrati principali'
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challengeType: 5
forumTopicId: 301910
dashedName: problem-261-pivotal-square-sums
---
# --description--
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Sia $k$ un numero intero positivo detto square-pivot se c'è una coppia di numeri interi $m > 0$ e $n ≥ k$, cossìcché la somma dei ($m + 1$) quadrati consecutivi fino a $k$ sia guale alla somma dei $m$ quadrati consecutivi a partire da ($n + 1$):
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$${(k - m)}^2 + \ldots + k^2 = {(n + 1)}^2 + \ldots + {(n + m)}^2$$
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Alcuni piccoli square-pivot sono
$$\begin{align} & \mathbf{4}: 3^2 + \mathbf{4}^2 = 5^2 \\\\ & \mathbf{21}: {20}^2 + \mathbf{21}^2 = {29}^2 \\\\ & \mathbf{24}: {21}^2 + {22}^2 + {23}^2 + \mathbf{24}^2 = {25}^2 + {26}^2 + {27}^2 \\\\ & \mathbf{110}: {108}^2 + {109}^2 + \mathbf{110}^2 = {133}^2 + {134}^2 \\\\ \end{align}$$
Trova la somma dei square pivot distinti $≤ {10}^{10}$.
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# --hints--
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`pivotalSquareSums()` dovrebbe restituire `238890850232021` .
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```js
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assert.strictEqual(pivotalSquareSums(), 238890850232021);
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```
# --seed--
## --seed-contents--
```js
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function pivotalSquareSums() {
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return true;
}
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pivotalSquareSums();
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```
# --solutions--
```js
// solution required
```