A type of algebraic factorization, of specific types of number (particularly a^n+/-b^n - see Cunningham Project), involving polynomials, particularly cyclotomic.
Some links:
http://mathworld.wolfram.com/AurifeuilleanFactorization.html
http://www.numericana.com/answer/numbers.htm#aurifeuille
http://www.ams.org/mcom/2006-75-253/S0025-5718-05-01766-7/home.html
http://perso.orange.fr/colin.barker/lpa/cycl_fac.htm
http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pd/rpb127.pdf
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