Sierpiński's Conjecture

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford (1998ab).

See also

Carmichael's Totient Function Conjecture

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Erdős, P. "Some Remarks on Euler's phi-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 10^(10000000)." Math. Comput. 63, 415-419, 1994.Schinzel, A. "Sur l'equation phi(x)=m." Elem. Math. 11, 75-78, 1956.

Cite this as:

Weisstein, Eric W. "Sierpiński's Conjecture." From MathWorld--A Wolfram Web Resource.

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