On diagonal equations over finite fields (Q5927546)
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scientific article; zbMATH DE number 1579928
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On diagonal equations over finite fields |
scientific article; zbMATH DE number 1579928 |
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On diagonal equations over finite fields (English)
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20 October 2002
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diagonal equations
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finite fields
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The authors obtain a sufficient condition for the diagonal equation NEWLINE\[NEWLINEa_1x_1^d + \cdots + a_nx_n^d =0NEWLINE\]NEWLINE to have only the trivial solution over finite fields. Their result improves previous results by \textit{N. Ankeny} and \textit{P. Erdős} [Am. J. Math. 76, 488-496 (1954; Zbl 0056.03505)] and \textit{Qi Sun} [J. Sichuan Normal Univ., Nat. Sci. Ed. 26, No. 2, 159-162 (1989; Zbl 0685.10011)]. They also prove that a conjecture posed by \textit{B. Powell} [J. Number Theory 18, 34-40 (1984; Zbl 0531.10017)] holds in a more general form.
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