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Diophantine Equations

  • Manfred R. Schroeder
Part of the Springer Series in Information Sciences book series (SSINF, volume 7)

Abstract

Diophantine equations, i.e., equations with integer coefficients for which integer solutions are sought, are among the oldest subjects in mathematics. Early historical occurrences often appeared in the guise of puzzles, and perhaps for that reason, Diophantine equations have been largely neglected in our mathematical schooling. Ironically, though, Diophantine equations play an ever-increasing role in modern applications, not to mention the fact that some Diophantine problems, especially the unsolvable ones, have stimulated an enormous amount of mathematical thinking, advancing the subject of number theory in a way that few other stimuli have.

Keywords

Integer Solution Diophantine Equation Triangular Number Room Acoustics Perfect Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 7.1
    G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers, 5th ed., Sect. 5. 4 ( Clarendon, Oxford 1984 )Google Scholar
  2. 7.2
    T. L. Heath: Diophantus of Alexandria ( Dover, New York 1964 )MATHGoogle Scholar
  3. 7.3
    C. F. Gauss: Disquisitiones Arithmeticae [English transi. by A. A. Clarke, Yale University Press, New Haven 1966 ]Google Scholar
  4. 7.4
    R. Tijdeman: On the equation of Catalan. Acta Arith. 29, 197–209 (1976);MathSciNetGoogle Scholar
  5. R. Tijdeman: “Exponential Diophantine Equations,” in Proc. Int. Congr. Math., Helsinki (1978)Google Scholar
  6. 7.5
    W. Kaufmann-Bühler: Gauss. A Biographical Study (Springer, Berlin, Heidelberg, New York (1981)Google Scholar
  7. 7.6
    M. Abramowitz, I. A. Stegun: Handbook of Mathematical Functions ( Dover, New York 1965 )Google Scholar
  8. 7.7
    M. D. Hirschhorn: A simple proof of Jacobi’s four-square theorem. J. Austral. Math. Soc. 32, 61–67 (1981)MathSciNetCrossRefGoogle Scholar
  9. 7.8
    H. Minkowski: Peter Gustav Lejeune Dirichlet und seine Bedeutung fur die heutige Mathematik. Jahresbericht der Deutschen Mathematiker-Vereinigung 14, 149–163 (1905)MATHGoogle Scholar
  10. 7.9
    M. R. Schroeder: Eigenfrequenzstatistik und Anregungsstatistik in Räumen. Acustica 4, 45–68 (1954)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenFed. Rep. of Germany
  2. 2.Acoustics Speech and Mechanics ResearchBell LaboratoriesMurray HillUSA

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