Abstract. It is shown that certain cubic polynomials with only real roots belong to the set of CNS polynomials. The results support a conjecture of B. Kovács and A. Pethő (1991) on bases of canonical number systems in real cubic number fields.

AMS Subject Classification (1991): 11A63, 11C08, 11R04, 11R16, 12D99

Received December 30, 2003, and in final form April 18, 2004. (Registered under 5827/2009.)