Uniform Distribution of Fractional Parts Related to Pseudoprimes
نویسندگان
چکیده
We estimate exponential sums with the Fermat-like quotients fg(n) = gn−1 − 1 n and hg(n) = gn−1 − 1 P (n) , where g and n are positive integers, n is composite, and P (n) is the largest prime factor of n. Clearly, both fg(n) and hg(n) are integers if n is a Fermat pseudoprime to base g, and this is true for all g coprime to n when for any Carmichael number n. On the other hand, our bounds imply that the fractional parts {fg(n)} and {hg(n)} are uniformly distributed, on average over g for fg(n), and individually for hg(n). AMS Subject Classification: 11L07, 11N37, 11N60
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