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Most of the unsolved problems are related to distribution of Gaussian primes in the plane.
*[[Gauss's circle problem]] does not deal with the Gaussian integers per se, but instead asks for the number of [[integer lattice point]]s inside a circle of a given radius centered at the origin. This is equivalent to determining the number of Gaussian integers with norm less than a given value.
There are also conjectures and unsolved problems about the Gaussian primes. Two of them are:
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