Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the second smallest prime $ k$th power nonresidue


Author: Richard H. Hudson
Journal: Proc. Amer. Math. Soc. 46 (1974), 343-346
MSC: Primary 10H35
MathSciNet review: 0364139
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Upper bounds for the second smallest prime $ k$th power nonresidue, which we denote by $ {g_2}(p,k)$, have been given by many authors. Theorem 1 represents an improvement of these bounds, at least for odd $ k$. We also give specific estimates for $ {g_2}(p,k)$, and an upper bound for the $ n$th $ (n \geq 2)$ smallest prime $ k$th power nonresidue as a function of the first $ n - 1$ prime nonresidues. Upper bounds for $ {g_2}(p,k)$ should take on new interest since the author has shown elsewhere that the first two consecutive $ k$th power nonresidues are bounded above by the product of the first two prime nonresidues.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10H35

Retrieve articles in all journals with MSC: 10H35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0364139-6
Article copyright: © Copyright 1974 American Mathematical Society