Missouri Journal of Mathematical Sciences

Gaussian Amicable Pairs

Patrick Costello and Ranthony A. C. Edmonds

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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.

Article information

Source
Missouri J. Math. Sci., Volume 30, Issue 2 (2018), 107-116.

Dates
First available in Project Euclid: 7 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1544151688

Digital Object Identifier
doi:10.35834/mjms/1544151688

Mathematical Reviews number (MathSciNet)
MR3884733

Zentralblatt MATH identifier
07063847

Subjects
Primary: 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas 11R27: Units and factorization

Keywords
amicable numbers Gaussian primes sum of divisors

Citation

Costello, Patrick; Edmonds, Ranthony A. C. Gaussian Amicable Pairs. Missouri J. Math. Sci. 30 (2018), no. 2, 107--116. doi:10.35834/mjms/1544151688. https://projecteuclid.org/euclid.mjms/1544151688


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References

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