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2005-2: Primality testing and Gaussian Sums
by Ciaran Mac an Bhaird.
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ISBN: 0-9544269-3-2
Publication date: 31 March, 2005.
Paperback. iv plus 120 pp. 295x210mm.
Retail Price: Euro 19.99.
This monograph is an introduction
to the background mathematics involved in
determining whether a given number is
prime or composite.
The first few chapters deal with basic probabilistic
primality tests using modular arithmetic. The author
then develops the theory of quadratic and cubic residue symbols
and the associated recoprocity laws.
These topics are investigated thoroughly using
Gauss and Jacobi sums, as well as Eisenstein integers and
multiplicative characters. The final chapter
gives a brief description of the deterministic
APR (Adleman, Pommerance and Rumely)
primality test.
The book, based on the author's Masters thesis, is
suitable for advanced undergraduate or postgraduate
student use. It should be useful to students with an interest
in number theory, Gauss sums, or primality testing in general.
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