On sum-sets and product-sets of complex numbers
We give a simple argument that for any finite set of complex numbers , the size of the the sum-set, , or the product-set, , is always large.
We give a simple argument that for any finite set of complex numbers , the size of the the sum-set, , or the product-set, , is always large.
In this paper we prove the following theorems in incidence geometry. 1. There is such that for any , and , if there are many distinct lines between and for all , , then are collinear. If the number of the distinct lines is then the cross ratio of the four points is algebraic. 2. Given , there is such that for any noncollinear, and , if there are many distinct lines between and for all , , then for any , we have distinct lines between and . 3. Given , there is...
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