  Let $q$ be a large prime number, $a$ be any integer, $\epsilon$ be a fixed
small positive quantity. Friedlander and Shparlinksi \cite{FSh} have shown that
there exists a positive integer $n\ll q^{5/2+\epsilon}$ such that $\phi(n)$
falls into the residue class $a \pmod q.$ Here, $\phi(n)$ denotes Euler's
function. In the present paper we improve this bound to $n\ll q^{2+\epsilon}.$
