freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-261-pivotal-square-sums.md

id, title, challengeType, forumTopicId, dashedName

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.

assert.strictEqual(pivotalSquareSums(), 238890850232021);

--seed--

--seed-contents--

function pivotalSquareSums() {

  return true;
}

pivotalSquareSums();

--solutions--

// solution required