For any non-integral positive real number c, any sequence (left peependicular n(c) right perpndicular)(n) is called a Pjateckii-Sapiro sequence. Given a real number c in the interval (1, 12/11), it is known that the number of primes in this sequence up to x has an asymptotic formula. We would like to use the techniques of Gupta and Murty to study Artin's problems for such primes. We will prove that even though the set of Pjateckii-Sapiro primes is of density zero for a fixed c, one can show that there exist natural numbers which are primitive roots for infinitely many Pjateckii-Sapiro primes for any fixed c in the interval (1, root 77/7 - 1/4) 7
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Pomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USAPomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USA
Garcia, Stephan Ramon
Kahoro, Elvis
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Pomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USAPomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USA
Kahoro, Elvis
Luca, Florian
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Univ Witwatersrand, Sch Math, Johannesburg, South Africa
Max Planck Inst Math, Bonn, Germany
Univ Ostrava, Fac Sci, Dept Math, Ostrava, Czech RepublicPomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USA