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Concept in number theory
In number theory, an aurifeuillean factorization, named after Léon-François-Antoine Aurifeuille, is factorization of certain integer values of the cyclotomic
Aurifeuillean_factorization
Decomposition of a number into a product
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
Integer_factorization
Mathematical project in integer factorization
the base), aurifeuillean factorization may be used, which gives a product of two or three numbers. The following equations give aurifeuillean factors for
Cunningham_Project
have Aurifeuillean factorizations, which can assist in finding prime factors. Cyclotomic polynomials are also helpful in finding factorizations. The amount
Binomial_number
Mathematical identity of polynomials
identity Aurifeuillean factorization Congruum, the shared difference of three squares in arithmetic progression Conjugate (algebra) Factorization "Difference
Difference_of_two_squares
Numbers that contain only the digit 1
situation is b = −4k4, with k positive integer, which has the aurifeuillean factorization, for example, b = −4 (with k = 1, then R2 and R3 are primes)
Repunit
Mathematical polynomial formula
Difference of two squares Binomial number Sophie Germain's identity Aurifeuillean factorization Fermat's Last Theorem McKeague, Charles P. (1986). Elementary
Sum_of_two_cubes
Irreducible polynomial whose roots are nth roots of unity
given by the coefficients of the numerator. Cyclotomic field Aurifeuillean factorization Zsigmondy number Root of unity Roman, Steven (2008), Advanced
Cyclotomic_polynomial
Mathematical polynomial factorization
{\displaystyle \Phi _{4}} as a polynomial, making this an example of an aurifeuillean factorization. Germain's identity has been generalized to the functional equation
Sophie_Germain's_identity
French mathematician
Aurifeuille (1822–1882) was a French mathematician after whom Aurifeuillean factorizations are named. He was the author of three books: Cours de géométrie
Léon-François-Antoine Aurifeuille
Léon-François-Antoine_Aurifeuille
Prime number of the form (2ᵖ+1)/3
OEIS)), where we have the aurifeuillean factorization. However, when b {\displaystyle b} does not admit an algebraic factorization, it is conjectured that
Wagstaff_prime
Odd number with specific properties
a covering set for all values of n. His proof depends on the aurifeuillean factorization t4⋅24m+2 + 1 = (t2⋅22m+1 + t⋅2m+1 + 1)⋅(t2⋅22m+1 − t⋅2m+1 + 1)
Sierpiński_number
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AURIFEUILLEAN FACTORIZATION
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AURIFEUILLEAN FACTORIZATION
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