---
id: 5900f47e1000cf542c50ff90
title: 'Problem 273: Sum of Squares'
challengeType: 5
forumTopicId: 301923
dashedName: problem-273-sum-of-squares
---

# --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.

# --hints--

`euler273()` should return 2032447591196869000.

```js
assert.strictEqual(euler273(), 2032447591196869000);
```

# --seed--

## --seed-contents--

```js
function euler273() {

  return true;
}

euler273();
```

# --solutions--

```js
// solution required
```