Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients

Autor:	Harman, Glyn, Shparlinski, Igor E.
Rok vydání:	2014
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	We show that for any $\varepsilon > 0$ and a sufficiently large cube-free $q$, any reduced residue class modulo $q$ can be represented as a product of $14$ integers from the interval $[1, q^{1/4e^{1/2} + \varepsilon}]$. The length of the interval is at the lower limit of what is possible before the Burgess bound on the smallest quadratic nonresidue is improved. We also consider several variations of this result and give applications to Fermat quotients.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1408.4515 Zobrazit plný text záznamu View this record from Arxiv