Least totient in a residue class | Zendy

Friedlander John B. | Zendy; Shparlinski Igor E. | Zendy

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Least totient in a residue class

Author(s) -

Friedlander John B.,

Shparlinski Igor E.

Publication year - 2007

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdm027

Subject(s) - euler's totient function , mathematics , modulo , residue (chemistry) , euler's formula , combinatorics , complement (music) , pure mathematics , class (philosophy) , discrete mathematics , mathematical analysis , biochemistry , chemistry , complementation , gene , phenotype , artificial intelligence , computer science

For a given residue class a ± od m with gcd( a , m ) = 1, upper bounds are obtained on the smallest value of n with φ( n ) ≡ a ± od m . Here, as usual φ( 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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