Something odd i noticed while playing around with primes.(adsbygoogle = window.adsbygoogle || []).push({});

We have the set of prime numbers P and a p ∈ P.

Define a function f:Q → N that will give the period of the repetition in the decimal expansion of some number r ∈ Q.

1) ∀ p ∈ P: ∃ n ∈ N: ∀ q ∈ P, q < p: f(q/p) = n.

So n is independant of q.

So define a function g:N → N: ∀ p ∈ P, ∀ q ∈ P, q < p: g(p) = f(q/p).

2) ∀ p ∈ P: ((p - 1) / g(p)) ∈ N.

You'll always get a unit fraction 1/2, 1/3, 1/4... never something like 5/7.

I was wondering why?

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# Prime division & repetition period

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