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On Carmichael's conjecture


Author: Carl Pomerance
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
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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 [Enhancements On Off] (What's this?)

  • [1] R. D. Carmichael, Note on Euler's $ \varphi $-function, Bull. Amer. Math. Soc. 28 (1922), 109-110. MR 1560520
  • [2] V. L. Klee, Jr., On a conjecture of Carmichael, Bull. Amer. Math. Soc. 53 (1947), 1183-1186. MR 9, 269. MR 0022855 (9:269d)
  • [3] A. Schinzel and W. Sierpiński, Sur certaines hypothèses concernant les nombres premiers, Acta Arith. 4 (1958), 185-208. MR 21 #4936.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0340161-0
Keywords: Euler $ \varphi $-function
Article copyright: © Copyright 1974 American Mathematical Society

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