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- W1635316243 abstract "We give a new elementary proof of the fact that the value of the least $k^{th}$ power non-residue in an arithmetic progression ${bn+c}_{n=0,1...}$, over a prime field $F_p$, is bounded by $7/sqrt{5} cdot b cdot sqrt{p/k} + 4b + c$. Our proof is inspired by the so called emph{Stepanov method}, which involves bounding the size of the solution set of a system of equations by constructing a non-zero low degree auxiliary polynomial that vanishes with high multiplicity on the solution set. The proof uses basic algebra and number theory along with a determinant identity that generalizes both the Sylvester and the Vandermonde determinant." @default.
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- W1635316243 date "2011-04-23" @default.
- W1635316243 modified "2023-09-24" @default.
- W1635316243 title "Square root Bound on the Least Power Non-residue using a Sylvester-Vandermonde Determinant" @default.
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