In number theory, an aurifeuillean factorization, named after Léon-François-Antoine Aurifeuille, is factorization of certain integer values of the cyclotomic polynomials.[1] Because cyclotomic polynomials are irreducible polynomials over the integers, such a factorization cannot come from an algebraic factorization of the polynomial. Nevertheless, certain families of integers coming from cyclotomic polynomials have factorizations given by formulas applying to the whole family, as in the examples below.
In number theory, an aurifeuilleanfactorization, named after Léon-François-Antoine Aurifeuille, is factorization of certain integer values of the cyclotomic...
called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer...
situation is b = −4k4, with k positive integer, which has the aurifeuilleanfactorization, for example, b = −4 (with k = 1, then R2 and R3 are primes)...
the base), aurifeuilleanfactorization may be used, which gives a product of two or three numbers. The following equations give aurifeuillean factors for...
identity Aurifeuilleanfactorization Congruum, the shared difference of three squares in arithmetic progression Conjugate (algebra) Factorization Complex...
Difference of two squares Binomial number Sophie Germain's identity Aurifeuilleanfactorization Fermat's last theorem McKeague, Charles P. (1986). Elementary...
Dirichlet's theorem on arithmetic progressions. Cyclotomic field Aurifeuilleanfactorization Root of unity Roman, Stephen (2008), Advanced Linear Algebra...
OEIS)), where we have the aurifeuilleanfactorization. However, when b {\displaystyle b} does not admit an algebraic factorization, it is conjectured that...
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