Missouri Journal of Mathematical Sciences

Gaussian Amicable Pairs

Patrick Costello and Ranthony A. C. Edmonds

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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

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

First available in Project Euclid: 7 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

amicable numbers Gaussian primes sum of divisors


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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