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November 2018 Gaussian Amicable Pairs
Patrick Costello, Ranthony A. C. Edmonds
Missouri J. Math. Sci. 30(2): 107-116 (November 2018). DOI: 10.35834/mjms/1544151688

Abstract

This article defines amicable pairs in the complex numbers and finds that some amicable pairs in the natural numbers are also amicable in the complex numbers. Unlike the case in the natural numbers, it is proved that no $(2,1)$ pairs made up of natural numbers where the common factor is a power of $2$ exist as Gaussian amicable pairs. Many pairs are found with complex parts using the DivisorSigma function in Mathematica. The factorizations into primes is given so that the type of pair might be determined.

Citation

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Patrick Costello. Ranthony A. C. Edmonds. "Gaussian Amicable Pairs." Missouri J. Math. Sci. 30 (2) 107 - 116, November 2018. https://doi.org/10.35834/mjms/1544151688

Information

Published: November 2018
First available in Project Euclid: 7 December 2018

zbMATH: 07063847
MathSciNet: MR3884733
Digital Object Identifier: 10.35834/mjms/1544151688

Subjects:
Primary: 11R04
Secondary: 11A25, 11R27

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 2 • November 2018
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