Description: |
We characterize the pairs (A,B) of finite non-empty subsets of a field such that the product-set, AB, is periodic and both the sumset, A+B, and the product-set, AB, are as small as possible, that is, |A+B|=min{p, |A|+|B|-1} and |AB|=max{|A|,|B|}, where p is the characteristic of the underlying field in nonzero characteristic and p=+oo otherwise.
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