Least totient in a residue class

John B. Friedlander; Igor E. Shparlinski

doi:10.1112/blms/bdm027

Least totient in a residue class

John B. Friedlander, Igor E. Shparlinski

School of Computing

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	425-432
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	39
Issue number	3
DOIs	https://doi.org/10.1112/blms/bdm027 https://doi.org/10.1112/blms/bdn037
Publication status	Published - 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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AU - Friedlander, John B.

AU - Shparlinski, Igor E.

N1 - Corrigendum can be found in Bulletin of the London Mathematical Society, Volume 40(3), 532, http://dx.doi.org/10.1112/blms/bdn037

PY - 2007/6

Y1 - 2007/6

N2 - 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'.

AB - 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'.

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ER -

Least totient in a residue class

Abstract

Bibliographical note

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