Some Divisibility Properties of the Euler Function
Let '(・) denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as a n ≡ 1 (mod '(n)), and we estimate the number of positive integers n ≤ x satisfying these conditions.
Glasgow Math. J. 47 (2005), no.3, 517-528.