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Number theory
Artin Primitive Roots Conjecture - part i
**Artin's Conjecture on Primitive Roots**, first half.
Let a be an integer that is not a square number and not −1. Then the set S(a)
of primes p such that a is a primitive root modulo
p
has a positive asymptotic
density inside the set of primes. In particular,
S(a)
is infinite.
$2,735 bounty·nobody has started
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Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
[Ho67] Hooley, C. "On Artin's conjecture." Journal für die reine und angewandte Mathematik 225 (1967): 209-220.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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