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In earlier papers Sárközy studied the solvability of the equations $$a + b = cd, a \in \mathcal{A}, b \in \mathcal{B}, c \in \mathcal{C}, d \in \mathcal{D},$$ resp. $$ab + 1 = cd, a \in \mathcal{A}, b \in \mathcal{B}, c \in \mathcal{C}, d \in \mathcal{D}$$ where $$\mathcal{A},\mathcal{B},\mathcal{C},\mathcal{D}$$ are “large” subsets of $$\mathbb{F}_p$$ . Later Gyarmati and Sárközy...
Many results have been proved on the distribution of the primitive roots. These results reflect certain random type properties of the set Gp of the primitive roots modulo p. This fact motivates the question that in what extent behaves Gp as a random subset of ℤp? First a much more general form of this problem is studied by using the notion of pseudo-randomness of subsets of ℤn which has...
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