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Finite or Infinite Number of Solutions of Polynomial Congruences in Two Positive Integer Variables

  • Thomas BierEmail author
Conference paper
  • 640 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 115)

Abstract

We give some conditions for polynomial systems of integer congruences to have infinitely or finitely many solutions in positive integers. Some of these conditions use the degrees of the polynomial, while others are more specific cases for certain special polynomials, mainly quadratic or cubic.

Keywords

Polynomial Congruences Positive Integer Solutions Biquadratic Case Nonnegative Integer-valued Function General Existence Result 
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Notes

Acknowledgements

I should like to thank the referee for useful comments on a previous version of this text. My particular gratitude goes to Prof Bernhard Heim for the opportunity to contribute to the wonderful Oman conference of GUTech in 2012, for his untiring commitment before, during and after this conference, and for his patience with my efforts during the preparation of this paper.

References

  1. 1.
    T. Bier, Non Standard Topics in Number Theory: Division Systems. Lecture Notes (University of Malaysia, KL, Malaysia, 2004)Google Scholar
  2. 2.
    T. Bier, O. Dira, Construction of integer sequences (submitted)Google Scholar
  3. 3.
    Online Encyclopedia of Integer Sequences. Sequences A 002310, A 002320 (contributed by C. Kimberling) and A003818 ff (contributed by W Pompe) in the website www.oeis.org
  4. 4.
    T. Bier, Classifications of solutions of certain biquadratic division systems (submitted)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BotswanaGaboroneBotswana
  2. 2.OldenburgGermany

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