Infinite families of noncototients

Flammenkamp, A.; Luca, F.

Colloquium Mathematicae, Tome 84/85 (2000), p. 37-41 / Harvested from The Polish Digital Mathematics Library

Résumé

For any positive integer $n$ let ϕ(n) be the Euler function of n. A positive integer $n$ is called a noncototient if the equation x-ϕ(x)=n has no solution x. In this note, we give a sufficient condition on a positive integer k such that the geometrical progression ${(2^{m} k)}_{m \geq 1}$ consists entirely of noncototients. We then use computations to detect seven such positive integers k.

Publié le : 2000-01-01

Zbl 0965.11003

EUDML-ID : urn:eudml:doc:210840

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     author = {A. Flammenkamp and F. Luca},
     title = {Infinite families of noncototients},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {37-41},
     zbl = {0965.11003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p37bwm}
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Flammenkamp, A.; Luca, F. Infinite families of noncototients. Colloquium Mathematicae, Tome 84/85 (2000) pp. 37-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p37bwm/

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