1.2 KiB
1.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4711000cf542c50ff84 | Problem 261: Pivotal Square Sums | 5 | 301910 | problem-261-pivotal-square-sums |
--description--
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:
{(k - m)}^2 + \ldots + k^2 = {(n + 1)}^2 + \ldots + {(n + m)}^2
Some small square-pivots are
\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}$$
Find the sum of all distinct square-pivots $≤ {10}^{10}$.
# --hints--
`pivotalSquareSums()` should return `238890850232021`.
```js
assert.strictEqual(pivotalSquareSums(), 238890850232021);
```
# --seed--
## --seed-contents--
```js
function pivotalSquareSums() {
return true;
}
pivotalSquareSums();
```
# --solutions--
```js
// solution required
```