Least totient in a residue class

John B. Friedlander, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


For a given residue class a (mod m) with gcd(a,m) = 1, upper bounds are obtained on the smallest value of n with (n) = a (mod m). Here, as usual (n) denotes the Euler function. These bounds complement a result of W. Narkiewicz on the asymptotic uniformity of distribution of values of the Euler function in reduced residue classes modulo m. Some discussion and results are also given for classes with gcd(a, m) > 1, in which case such n do not always exist, and also on the related problem for 'cototients'.

Original languageEnglish
Pages (from-to)425-432
Number of pages8
JournalBulletin of the London Mathematical Society
Issue number3
Publication statusPublished - Jun 2007

Bibliographical note

Corrigendum can be found in Bulletin of the London Mathematical Society, Volume 40(3), 532, http://dx.doi.org/10.1112/blms/bdn037

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