The conjecture that all integers occur as a value of the totient valence function (i.e., all integers occur as multiplicities). The conjecture was proved by Ford (1998ab).

# Sierpiński's Conjecture

## See also

Carmichael's Totient Function Conjecture## Explore with Wolfram|Alpha

## References

Erdős, P. "Some Remarks on Euler's -Function."*Acta Arith.*

**4**, 10-19, 1958.Ford, K. "The Distribution of Totients."

*Ramanujan J.*

**2**, 67-151, 1998a.Ford, K. "The Distribution of Totients,

*Electron. Res. Announc. Amer. Math. Soc.*

**4**, 27-34, 1998b.Guy, R. K.

*Unsolved Problems in Number Theory, 2nd ed.*New York: Springer-Verlag, p. 94, 1994.Schlafly, A. and Wagon, S. "Carmichael's Conjecture on the Euler Function is Valid Below ."

*Math. Comput.*

**63**, 415-419, 1994.Schinzel, A. "Sur l'equation "

*Elem. Math.*

**11**, 75-78, 1956.

## Cite this as:

Weisstein, Eric W. "Sierpiński's Conjecture."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/SierpinskisConjecture.html