How many different values of positive integer 'n' are there such that expansion of 1/n terminates when written in base 57 and 323 such that n < 10000.

In decimal system, numbers of the form 1/n are terminating if n is of the form 2^a * 5^b. So, in base 57, n should be of the form 3^a * 19^b. In base 323, n should be of the form 17^k * 19^p. Since the number should terminate in both the bases, n should be of the form 19^p (Common prime factor). Since n is less than 10000, the only possible values of p are 0, 1, 2 and 3 - a total of 4 values.

Answer = 4