On the smallest simultaneous power nonresidue modulo a prime
نویسندگان
چکیده
Let p be a prime and p1, . . . , pr be distinct prime divisors of p− 1. We prove that the smallest positive integer n which is a simultaneous p1, . . . , pr-power nonresidue modulo p satisfies n < p 1/4−cr+o(1) (p → ∞) for some positive cr satisfying cr = e −(1+o(1))r (r → ∞). Mathematical Subject Classification: 11A15, 11A07, 11N29
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