In this paper, we show that there are no planar functions from Z(3pq) to Z(
3pq) where p and q are distinct primes larger than 3. As a result, there ar
e only two undecided cases for planar functions from Z(n) to Z(n) if n is n
ot a prime and n less than or equal to 50,000. (C) 2000 Academic Press.