|Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.3|
Here, I consider the set of integers that can be written as a sum of two squares and develop an algorithm that constructs the minimal sets for congruence classes. In fact, this algorithm can be applied to a more general class of sets.
I show that minimal sets do not permit much structure, i.e., set-theoretic relations between two sets will, in general, not be passed on to the respective minimal sets. In addition to this, measure-theoretic tools cannot help in determining the number of elements in minimal sets.
Received October 1 2014; revised versions received March 26 2015. Published in Journal of Integer Sequences, May 19 2015.