# Math Help - Pairwise distinct primes

1. ## Pairwise distinct primes

Let n = p1.....pm for pairwise distinct primes pi other than 2 and 5. Let ki
be the period of the decimal expression of 1/pi. Show that the period of the decimal
expression of 1/n is the least common multiple of k1,....,km.

2. ## Re: Pairwise distinct primes

Hi,
The attachment should enable you to give a proof:

3. ## Re: Pairwise distinct primes

A proof of the first fact can be found in Elementary Number Theory by Dudley, which is available online.

Section 15, p. 118, Theorem 4. If (n, 10) = 1, then the period of 1/n is the order of 10 modulo n.