873 B
873 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f51d1000cf542c51002f | Problem 433: Steps in Euclid's algorithm | 5 | 302104 | problem-433-steps-in-euclids-algorithm |
--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).
--hints--
euler433()
should return 326624372659664.
assert.strictEqual(euler433(), 326624372659664);
--seed--
--seed-contents--
function euler433() {
return true;
}
euler433();
--solutions--
// solution required