# Problem 433: Steps in Euclid's algorithm
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).