Equalities between greatest common divisors involving three coprime pairs

Throughout their school careers, students are taught how to find the prime factorization of numbers. Most students readily learn the technique and find the process interesting. Most teachers then teach the ways in which prime factorizations can aid in factoring polynomials and finding greatest common divisors as well as least common multiples.

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GREATEST COMMON DIVISORS OF EUCLIDEAN DOMAIN MATRICES

Far East Journal of Mathematical Sciences (FJMS) ◽

10.17654/ms101040855 ◽

2017 ◽

Vol 101 (4) ◽

pp. 855-872

Author(s):

Nur Erawaty ◽

Mawardi Bahri ◽

Loecky Haryanto ◽

Amir Kamal Amir

Keyword(s):

Euclidean Domain ◽

Greatest Common Divisors

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Greatest Common Divisors of $u-1, v-1$ in positive characteristic and rational points on curves over finite fields

Journal of the European Mathematical Society ◽

10.4171/jems/409 ◽

2013 ◽

Vol 15 (5) ◽

pp. 1927-1942 ◽

Cited By ~ 10

Author(s):

Pietro Corvaja ◽

Umberto Zannier

Keyword(s):

Finite Fields ◽

Positive Characteristic ◽

Rational Points ◽

Curves Over Finite Fields ◽

Greatest Common Divisors

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Greatest common divisors from generalized sylvester resultant matrices

Linear and Multilinear Algebra ◽

10.1080/03081088008817332 ◽

1980 ◽

Vol 8 (4) ◽

pp. 271-279 ◽

Cited By ~ 19

Author(s):

Stephen Barnett

Keyword(s):

Sylvester Resultant ◽

Greatest Common Divisors

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Ordered groups with greatest common divisors theory

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171200004087 ◽

2000 ◽

Vol 24 (7) ◽

pp. 469-479

Author(s):

Jiří Močkoř

Keyword(s):

Abelian Group ◽

Ordered Groups ◽

Greatest Common Divisors

An embedding (called aGCD theory) of partly ordered abelian groupGinto abelian l-groupΓis investigated such that any element ofΓis an infimum of a subset (possible non-finite) fromG. It is proved that a GCD theory need not be unique. Acomplete GCD theoryis introduced and it is proved thatGadmits a complete GCD theory if and only if it admits a GCD theoryG→Γsuch thatΓis an Archimedean l-group. Finally, it is proved that a complete GCD theory is unique (up too-isomorphisms) and that a po-group admits the complete GCD theory if and only if anyv-ideal isv-invertible.

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