---
id: 5900f47e1000cf542c50ff90
challengeType: 5
title: 'Problem 273: Sum of Squares'
---

## Description
<section id='description'>
Consider equations of the form: a2 + b2 = N, 0 ≤ a ≤ b, a, b and N integer.

For N=65 there are two solutions:
a=1, b=8 and a=4, b=7.
We call S(N) the sum of the values of a of all solutions of a2 + b2 = N, 0 ≤ a ≤ b, a, b and N integer.
Thus S(65) = 1 + 4 = 5.
Find ∑S(N), for all squarefree N only divisible by primes of the form 4k+1 with 4k+1 < 150.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler273()</code> should return 2032447591196869000.
    testString: assert.strictEqual(euler273(), 2032447591196869000, '<code>euler273()</code> should return 2032447591196869000.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler273() {
  // Good luck!
  return true;
}

euler273();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>