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
Full paper (PDF, 134 Kb)

Details

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(n^2+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

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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.