freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-229-four-representations-using-squares.english.md

id	challengeType	title	forumTopicId
5900f4521000cf542c50ff64	5	Problem 229: Four Representations using Squares	301872

Description

Consider the number 3600. It is very special, because

3600 = 482 +     362 3600 = 202 + 2×402 3600 = 302 + 3×302 3600 = 452 + 7×152

Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.

In 1747, Euler proved which numbers are representable as a sum of two squares. We are interested in the numbers n which admit representations of all of the following four types:

n = a12 +   b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,

where the ak and bk are positive integers.

There are 75373 such numbers that do not exceed 107.

How many such numbers are there that do not exceed 2×109?

Instructions

Tests

tests:
  - text: <code>euler229()</code> should return 11325263.
    testString: assert.strictEqual(euler229(), 11325263);

Challenge Seed

function euler229() {
  // Good luck!
  return true;
}

euler229();

Solution

// solution required