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 ConjectureExplore 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