On computing factors of cyclotomic polynomials

Details On computing factors of cyclotomic polynomials On computing factors of cyclotomic polynomials

2010-04-30

arxiv.org/abs/1004.5466v1

Mathematics of Computation 61 (1993), 131-149.

Mathematics

Number Theory

21 pages. An old Technical Report, submitted for archival purposes. For further details, see http://wwwmaths.anu.edu.au/~brent

Scientific paper

For odd square-free n > 1 the n-th cyclotomic polynomial satisfies an identity of Gauss. There are similar identity of Aurifeuille, Le Lasseur and Lucas. These identities all involve certain polynomials with integer coefficients. We show how these coefficients can be computed by simple algorithms which require O(n^2) arithmetic operations and work over the integers. We also give explicit formulae and generating functions for the polynomials, and illustrate the application to integer factorization with some numerical examples.

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