Abstract
In this paper, we obtain new upper bounds for trigonometric sums over subgroups Γ ⊂ Z*p whose size belongs to [p28/95, p182/487]. Using an approach due to Malykhin, we refine estimates of such sums in \(\mathbb{Z}_{{p^r}}^*\) and apply them to the divisibility problem for Fermat quotients.
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