On diagonal equations over finite fields via walks in NEPS of graphs

2019/07/06 by Videla, Denis E.
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1907.03145

Abstract

In this paper, we obtain an explicit combinatorial formula for the number of solutions (x₁,…,x_r)∈ \mathbbF_p^ab to the diagonal equation x₁^k+⋯+x_r^k=α over the finite field \mathbbF_p^ab, with k=\fracp^ab-1b(p^a-1) and b>1 by using the number of r-walks in NEPS of complete graphs.

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