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Visible Points on Modular Exponential Curves

Tsz Ho Chan, Igor E. Shparlinski (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We obtain an asymptotic formula for the number of visible points (x,y), that is, with gcd(x,y) = 1, which lie in the box [1,U] × [1,V] and also belong to the exponential modular curves y a g x ( m o d p ) . Among other tools, some recent results of additive combinatorics due to J. Bourgain and M. Z. Garaev play a crucial role in our argument.

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