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math.NT2005
On the maximal order of numbers in the "factorisatio numerorum" problem
Martin Klazar, Florian Luca
Let m(n) be the number of ordered factorizations of n in factors larger than 1. We prove that for every eps>0 n^{rho} m(n) < exp[(log n)^{1/rho}/(loglog n)^{1+eps}] holds for all i…
math.NT2005
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…