Adult web hosting - 4.5.2 THE GREATEST COMMON DIVISOR 335 These experiments
4.5.2 THE GREATEST COMMON DIVISOR 335 These experiments showed a rather small standard deviation from the observed average values. The coefficients $ and 1 of m in (42) and (43) can be verified rigorously without using the lattice-point approximation (see exercise 21); so the error in the lattice-point model is apparently in the coefficient of n, which is too high. The above calculations have been made under the assumption that u and v are odd and in the ranges 2m 5 u < 2m+1 and 2n 2 v < 2n+1. If we assume instead that 1~ and v are to be any integers, independently and uniformly distributed over the ranges 12 IL< 2N, 1 2 v < 2N, then we can calculate the average values of C and D from the data already given; in fact, if C,, denotes the average value of C under our earlier assumptions, exercise 22 shows that we have (zN -1)2C = N2Coo + 2N c (N -n)2n-1C,0 l