Artin’s conjecture on primitive roots
Let be a number in the list or for some . Then we know that has a primitive root, but finding one can be a rather challenging problem (theoretically and computationally).
Gauss conjectured that the number is a primitive root for infinitely many primes . Much later, in , Emil Artin made the following conjecture:
Let be an integer not equal to or a square. Then is a primitive root for infinitely many primes .
However, up to now, nobody has been able to show that a single integer is a primitive root for infinitely many primes. It can be shown that the number is a primitive root for every Fermat prime but, unfortunately, the existence of infinitely many Fermat primes is far from obvious, and in fact it is quite dubious (only five Fermat primes are known!).
|Title||Artin’s conjecture on primitive roots|
|Date of creation||2013-03-22 16:21:04|
|Last modified on||2013-03-22 16:21:04|
|Last modified by||alozano (2414)|