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.

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- Aug 30th 2013, 06:33 AMyipyingPairwise 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. - Aug 30th 2013, 10:47 AMjohngRe: Pairwise distinct primes
Hi,

The attachment should enable you to give a proof:

Attachment 29093 - Aug 30th 2013, 12:13 PMemakarovRe: 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.