A note on the second smallest prime th power nonresidue

Author:
Richard H. Hudson

Journal:
Proc. Amer. Math. Soc. **46** (1974), 343-346

MSC:
Primary 10H35

DOI:
https://doi.org/10.1090/S0002-9939-1974-0364139-6

MathSciNet review:
0364139

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Abstract: Upper bounds for the second smallest *prime* th power nonresidue, which we denote by , have been given by many authors. Theorem 1 represents an improvement of these bounds, at least for odd . We also give specific estimates for , and an upper bound for the th smallest *prime* th power nonresidue as a function of the first *prime* nonresidues. Upper bounds for should take on new interest since the author has shown elsewhere that the first two consecutive th power nonresidues are bounded above by the product of the first two prime nonresidues.

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0364139-6

Article copyright:
© Copyright 1974
American Mathematical Society