Euler's equation \(\phi (x)=k\) with no solution
Let \(\phi\) denote the Euler totient function. The author finds two classes of values of k for which the equation \(\phi (x)=k\) has no solution in x. In both classes k is of the form \(2^ n p_ 1^{a(1)}... p_ m^{a(m)},\) where n, a(1),...,a(m) are positive integers and \(p_ 1,...,p_ m\) distinct odd primes satisfying certain conditions. The proofs are elementary.
scientific article; zbMATH DE number 4093542