caveman1917
- 33
- 3
Something odd i noticed while playing around with primes.
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 independent 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?
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 independent 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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