## order of 2 in Z_p

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• Greetings all, let o_p(2) = order of 2 in F_p. in other words, o_p(2) = card{ 2^0 (mod p), 2^1 (mod p), ... , 2^p (mod p) } we know that it is an open
Message 1 of 2 , Nov 15, 2009
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Greetings all,
let o_p(2) = order of 2 in F_p.
in other words, o_p(2) = card{ 2^0 (mod p), 2^1 (mod p), ... , 2^p (mod
p) }
we know that it is an open conjecture that o_p(2) = p-1 for p a
prime.but does anyone actually know what is:
limsup o_p(2)/p = ?where p goes over all primes?
thanks,

lou

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• ... Counterexample: o_137(2) = (137 - 1)/2 = 68 o_p(2) is provably a divisor of p-1 for prime p. By the Artin conjecture, it is a proper divisor of p-1 for
Message 2 of 2 , Nov 15, 2009
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"LEGalup" <legalup@...> wrote:

> let o_p(2) = order of 2 in F_p.
...
> o_p(2) = p-1 for p prime

Counterexample: o_137(2) = (137 - 1)/2 = 68

o_p(2) is provably a divisor of p-1 for prime p.
By the Artin conjecture, it is a proper divisor