quotients, primes, Gaussian primes, complex plane, dense
It has been observed many times, both in the Monthly and elsewhere, that the set of all quotients of prime numbers is dense in the positive real numbers. In this short note we answer the related question: "Is the set of all quotients of Gaussian primes dense in the complex plane?"
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Garcia, S.R., Quotients of Gaussian Primes, American Mathematical Monthly. 120 (2013), no. 9, 851-853.