Find the number of positive integers that divide (10)^999 but not (10)^998.

Breaking down the numbers:

10^999 = 2^999 * 5^999
10^998 = 2^998 * 5^998

The multiples for the first that do not appear in the second:

2^999 * 5^n for n = 1 to 999

and

5^999 * 2^m for m = 1 to 998 (999 is redundant)

999 + 998 = 1997 exclusive factors.

Posted by Leming on 2006-05-18 08:45:45