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gikf a9c11f7fe2 fix: clean-up Project Euler 421-440 (#43047 )

2021-07-29 11:14:09 -07:00

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f51d1000cf542c51002f	Problem 433: Steps in Euclid's algorithm	5	302104	problem-433-steps-in-euclids-algorithm

--description--

Let E(x_0, y_0) be the number of steps it takes to determine the greatest common divisor of x_0 and y_0 with Euclid's algorithm. More formally:

$$\begin{align} & x_1 = y_0, y_1 = x_0\bmod y_0 \\ & x_n = y_{n - 1}, y_n = x_{n - 1}\bmod y_{n - 1} \end{align}$$

E(x_0, y_0) is the smallest n such that y_n = 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) = 39\\,826.

Find S(5 \times {10}^6).

--hints--

stepsInEuclidsAlgorithm() should return 326624372659664.

assert.strictEqual(stepsInEuclidsAlgorithm(), 326624372659664);

function stepsInEuclidsAlgorithm() {

  return true;
}

stepsInEuclidsAlgorithm();

// solution required