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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’.