It is thought that the Totient Valence Function (i.e., the Totient Valence Function never takes the value 1). This assertion is called Carmichael's totient function conjecture and is equivalent to the statement that there exists an such that (Ribenboim 1996, pp. 39-40). Any counterexample to the conjecture must have more than 10,000 Digits (Conway and Guy 1996). Recently, the conjecture was reportedly proven by F. Saidak in November, 1997 with a proof short enough to fit on a postcard.

**References**

Conway, J. H. and Guy, R. K. *The Book of Numbers.* New York: Springer-Verlag, p. 155, 1996.

Ribenboim, P. *The New Book of Prime Number Records.* New York: Springer-Verlag, 1996.

© 1996-9

1999-05-26