The Waring’s problem over finite fields through generalized Paley graphs
نویسندگان
چکیده
We show that the Waring number over a finite field Fq, denoted as g(k,q), when exists coincides with diameter of generalized Paley graph ?(k,q)=Cay(Fq,Rk) Rk={xk:x?Fq?}. find infinite new families exact values g(k,q) from characterization graphs ?(k,q) which are also Hamming proved by Lim and Praeger in 2009. Then, we every positive integer is for some pair (k,q) q not prime. Finally, lower bound g(k,p) p prime using ?(k,p) circulant this case.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2021
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2021.112324