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Uniform Distribution of Fractional Parts Related to Pseudoprimes
William D. Banks, Moubariz Z. Garaev, Florian Luca +1
We estimate exponential sums with the Fermat-like quotients $$ f_g(n) = \frac{g^{n-1} - 1}{n} \mand h_g(n)=\frac{g^{n-1}-1}{P(n)}, $$ where and are positive integers, i…
Complexity of Inverting the Euler Function
Scott Contini, Ernie Croot, Igor Shparlinski
We present an algorithm to invert the Euler function . The algorithm, for a given , in polynomial time ``on average'', finds the set of all solutions to…
Prime divisors of sequences associated to elliptic curves
Graham Everest, Igor E Shparlinski
We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large valu…
Exponential Sums and Congruences with Factorials
Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski
We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials and…
Character Sums and Congruences with n!
Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski
We estimate character sums with n!, on average, and individually. These bounds are used to derive new results about various congruences modulo a prime p and obtain new information…