Bézout and Gauss

  • Olivier Bordellès
Part of the Universitext book series (UTX)


The theorems of Bachet–Bézout and Gauss are the cornerstones of elementary methods in number theory. Many applications of these results are studied, in particular Diophantine problems. The section Further Developments investigates the number of integer solutions of certain linear Diophantine equations, i.e. the number of certain restricted partitions of an integer.


  1. [BR04]
    Beck M, Robins S (2004) A formula related to the Frobenius problem in 2 dimensions. In: Chudnovsky D, Chudnovsky G, Nathanson M (eds) Number theory. New York seminar 2003. Springer, Berlin, pp 17–23 Google Scholar
  2. [BZ04]
    Beck M, Zacks S (2004) Refined upper bounds for the linear Diophantine problem of Frobenius. Adv Appl Math 32:454–467 MathSciNetzbMATHCrossRefGoogle Scholar
  3. [Gou72]
    Gould HW (1972) Combinatorial identities. A standardized set of tables listing 500 binomial coefficients summations. Morgantown, West Virginia Google Scholar
  4. [Odl95]
    Odlyzko AM (1995) Asymptotic enumeration methods. Elsevier, Amsterdam Google Scholar
  5. [Pop53]
    Popoviciu T (1953) Asupra unei probleme de patitie a numerelor. Stud Cercet Stiint—Acad RP Rom, Fil Cluj 4:7–58 Google Scholar
  6. [Shi06]
    Shiu P (2006) Moment sums associated with linear binary forms. Am Math Mon 113:545–550 MathSciNetzbMATHCrossRefGoogle Scholar
  7. [Tri00]
    Tripathi A (2000) The number of solutions to ax+by=n. Fibonacci Q 38:290–293 zbMATHGoogle Scholar
  8. [Wil90]
    Wilf HS (1990) Generatingfunctionology. Academic Press, New York zbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Olivier Bordellès
    • 1
  1. 1.AiguilheFrance

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