Euler's function in residue classes
The authors discuss the question if there are infinitely many values of Euler's function \(\varphi\) in a given residue class \(r\bmod m\). It is clear that this is not the case for a class not containing even numbers. In the paper under review it is proved that a residue class containing a multiple of 4 has this property. The authors point out that 4 cannot be replaced by 2. This is shown by \textit{K. Ford}, \textit{S. Konyagin} and \textit{C. Pomerance} [Number theory in progress, Zakopane, Poland 1997, Vol. 2, 805-812 (1999)]. Further the authors derive asymptotic formulas for the distribution of \(\varphi(n)\) in the residue classes mod 12.
scientific article; zbMATH DE number 1203254