Missouri Journal of Mathematical Sciences
- Missouri J. Math. Sci.
- Volume 30, Issue 2 (2018), 107-116.
Gaussian Amicable Pairs
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.
Missouri J. Math. Sci., Volume 30, Issue 2 (2018), 107-116.
First available in Project Euclid: 7 December 2018
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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