Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; doi:10.1007/978-0-387-26677-0. Section B37 "Does $\phi(n)$ properly divide $n-1$?" is on pp. 142--143; Graham's conjecture that for all $k$ there are infinitely many $n$ with $\phi(n)\mid(n-k)$ is on p. 143. Library home: Guy 2004.