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Recently, several bounds have been obtained on the number of solutions of congruences of the type (formula presented) where p is prime and variables take values in some short interval. Here, for almost all p and all s and also for a fixed p and almost all s, we derive stronger bounds. We also use similar ideas to show that for almost all p, one can always find an element of a large order in any rather short interval.
|Number of pages||31|
|Journal||Journal d'Analyse Mathematique|
|Publication status||Published - Oct 2014|
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