We show that for any ϵ > 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, q1/4 e1/2 + ϵ]. 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.
|Number of pages||23|
|Journal||International Mathematics Research Notices|
|Publication status||Published - 19 Jun 2016|