freeCodeCamp/problem-433-steps-in-euclids-algorithm.english.md at 3c3ceaa3f5a4164c5182a82f49842096cb027676

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Oliver Eyton-Williams f1c9b08cf3 fix(curriculum): add isHidden: false to challenges

This includes certificates (where it does nothing), but does not
include any translations.

2020-05-25 16:25:19 +05:30

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id, challengeType, isHidden, title, forumTopicId

id	challengeType	isHidden	title	forumTopicId
5900f51d1000cf542c51002f	5	false	Problem 433: Steps in Euclid's algorithm	302104

Description

Let E(x0, y0) be the number of steps it takes to determine the greatest common divisor of x0 and y0 with Euclid's algorithm. More formally:x1 = y0, y1 = x0 mod y0xn = yn-1, yn = xn-1 mod yn-1 E(x0, y0) is the smallest n such that yn = 0.

We have E(1,1) = 1, E(10,6) = 3 and E(6,10) = 4.

Define S(N) as the sum of E(x,y) for 1 ≤ x,y ≤ N. We have S(1) = 1, S(10) = 221 and S(100) = 39826.

Find S(5·106).

Instructions

Tests

tests:
  - text: <code>euler433()</code> should return 326624372659664.
    testString: assert.strictEqual(euler433(), 326624372659664);

Challenge Seed

function euler433() {
  // Good luck!
  return true;
}

euler433();

Solution

// solution required

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