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.
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References
T. Bier, Non Standard Topics in Number Theory: Division Systems. Lecture Notes (University of Malaysia, KL, Malaysia, 2004)
T. Bier, O. Dira, Construction of integer sequences (submitted)
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
T. Bier, Classifications of solutions of certain biquadratic division systems (submitted)
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.
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© 2014 Springer International Publishing Switzerland
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Bier, T. (2014). Finite or Infinite Number of Solutions of Polynomial Congruences in Two Positive Integer Variables. In: Heim, B., Al-Baali, M., Ibukiyama, T., Rupp, F. (eds) Automorphic Forms. Springer Proceedings in Mathematics & Statistics, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-11352-4_2
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DOI: https://doi.org/10.1007/978-3-319-11352-4_2
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