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- W4226502199 abstract "<abstract><p>Let $ p $ be a prime, $ k $ a positive integer, $ q = p^k $, and $ mathbb{F}_q $ be the finite field with $ q $ elements. In this paper, by using the Jacobi sums, we give an explicit formula for the number of solutions of the two-variable diagonal sextic equations $ x_1^6+x_2^6 = c $ over $ mathbb{F}_q $, with $ cinmathbb{F}_q^* $ and $ pequiv1({rm{mod}} 6) $. Furthermore, by using the reduction formula for Jacobi sums, the number of solutions of the diagonal sextic equations $ x_1^6+x_2^6+cdots+x_n^6 = c $ of $ ngeq3 $ variables with $ cinmathbb{F}_q^* $ and $ pequiv1({rm{mod}} 6) $, can also be deduced.</p></abstract>" @default.
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- W4226502199 date "2022-01-01" @default.
- W4226502199 modified "2023-09-30" @default.
- W4226502199 title "On the number of solutions of two-variable diagonal sextic equations over finite fields" @default.
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- W4226502199 doi "https://doi.org/10.3934/math.2022588" @default.
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