INTEGERS : ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 6 ( 2006 ) , # A 06 ON THE EQUATION m − 1 = aφ ( m )

Let φ denote Euler’s totient function. It is shown that if r ≥ 2 there exist only finitely many positive integers n such that φ(n) divides n − 1 and φ(n)2 ≡ r (mod n). It is also shown that if k ≥ 2 there exist only finitely many positive integers n such that φ(n) divides n − 1 and φ(n)k ≡ 1 (mod n).