## Missouri Journal of Mathematical Sciences

### Gaussian Amicable Pairs

#### 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

https://projecteuclid.org/euclid.mjms/1544151688

Digital Object Identifier
doi:10.35834/mjms/1544151688

Mathematical Reviews number (MathSciNet)
MR3884733

Zentralblatt MATH identifier
07063847

#### 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

#### References

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