Congruences and rational exponential sums with the Euler function

William D. Banks*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We give upper bounds for the number of solutions to congruences with the Euler function φ(n) modulo an integer q ≥ 2. We also give nontrivial bounds for rational exponential sums with φ(n)/q.

Original languageEnglish
Pages (from-to)1415-1426
Number of pages12
JournalRocky Mountain Journal of Mathematics
Issue number5
Publication statusPublished - 2006


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