Abstract
This work is about the generalization of sum-product problem. The general principle of it was formulated in the Erdos-Szemeredi’s hypothesis. Instead of the Minkowski sum in this hypothesis, the set of values f(x,y) of a homogeneous polynomial f lin two variables, where x and y belong to subgroup G of is considered. The lower bound on the cardinality of such set is obtained. This topic has an applied value in the theory of information and dynamics in calculating the probabilities of events, as well as in various methods of encoding and decoding information.
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