by Christiaan van de Woestijne

**Abstract:**

Deterministic algorithms are presented for the efficient solution of
diagonal homogeneous equations in many variables over finite fields. As
auxiliary algorithms, it is shown how to compute a field generator that is an
*n*th power, and how to write elements as sums of *n*th powers, for a given
integer *n*. All these algorithms take polynomial time in *n* and in the
logarithm of the field size, and are practical as stated.

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© ACM, 2005. This is the author's version of the work. It is posted here
by permission of ACM for your personal use. Not for redistribution. The
definitive version was published in *Proceedings of the 2005 International
Symposium on Symbolic and Algebraic Computation* (ISSAC'05, Beijing, China),
July 2005, pp. 348-353, http://doi.acm.org/10.1145/1073884.1073932.