Conductors for sets of large integer squares

Ken Dutch and Christy Rickett
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 18, 2012, Number 1, Pages 16—21
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Authors and affiliations

Ken Dutch

Department of Mathematics and Statistics
Eastern Kentucky University
Richmond, Kentucky 40475, USA

Christy Rickett

Department of Mathematics and Statistics
Eastern Kentucky University
Richmond, Kentucky 40475, USA

Abstract

We calculate the Frobenius conductor for the infinite set {n2, (n + 1)2, …} through n = 200, demonstrate that the conductor’s growth rate as function of n is o(n2+ε) for any positive ε, and calculate specific numerical bounds for several ε > 0.0145.

Keywords

  • Frobenius Coin Problem
  • Conductor
  • Lagrange Four Square Theorem
  • Diophantine Equations

AMS Classification

  • 11D07
  • 11P05

References

  1. Brauer, A. J. E. Shockley, On a problem of Frobenius, J. reine angew. Math. Vol. 211, 1962, 215–220.
  2. Burton, D.W., Elementary Number Theory. Allyn and Bacon, Inc., 1980.
  3. Hardy, G. H., E. M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, London, 1962.
  4. Nijenhuis, A., H. S. Wilf, Representations of integer by linear forms in nonnegative integers, J. Number Theory. Vol. 4, 1972, 98–106
  5. Sylvester, J. J. Questions 7382, Mathematical Questions from the Educational Times. Vol. 37, 1884, 26.

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Cite this paper

APA

Dutch, K., & Rickett, C. (2012). Conductors for sets of large integer squares, Notes on Number Theory and Discrete Mathematics, 18(1), 16-21.

Chicago

Dutch, Ken, and Christy Rickett. “Conductors for Sets of Large Integer Squares.” Notes on Number Theory and Discrete Mathematics 18, no. 1 (2012): 16-21.

MLA

Dutch, Ken, and Christy Rickett. “Conductors for Sets of Large Integer Squares.” Notes on Number Theory and Discrete Mathematics 18.1 (2012): 16-21. Print.

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