Dear readers! Let m = (b^n-1)/(b-1). Theorem: if m == 1 (mod n), then b^(m-1) == 1 (mod m). Conjecture: if b^(m-1) == 1 (mod m), then m == 1 (mod n). I am asking for proof or a counterexample. Best regards, Thomas Ordowski __________________ http://oeis.org/history/view?seq=A005935&v=64 See my comment and the reference to Steuerwald.