On Carmichael’s conjecture
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- by Carl Pomerance
- Proc. Amer. Math. Soc. 43 (1974), 297-298
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340161-0
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Abstract:
A sufficient condition is given for a natural number $x$ in order that the equation $\varphi (x) = \varphi (y)$ has only the solution $y = x$. It is conjectured that no natural numbers satisfy this sufficient condition.References
- R. D. Carmichael, Note on Euler’s $\varphi$-function, Bull. Amer. Math. Soc. 28 (1922), no. 3, 109–110. MR 1560520, DOI 10.1090/S0002-9904-1922-03504-5
- V. L. Klee Jr., On a conjecture of Carmichael, Bull. Amer. Math. Soc. 53 (1947), 1183–1186. MR 22855, DOI 10.1090/S0002-9904-1947-08940-0 A. Schinzel and W. Sierpiński, Sur certaines hypothèses concernant les nombres premiers, Acta Arith. 4 (1958), 185-208. MR 21 #4936.
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 297-298
- MSC: Primary 10A20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340161-0
- MathSciNet review: 0340161