# Infinite families of noncototients

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 1, page 37-41
- ISSN: 0010-1354

## Access Full Article

top## Abstract

top## How to cite

topFlammenkamp, A., and Luca, F.. "Infinite families of noncototients." Colloquium Mathematicae 86.1 (2000): 37-41. <http://eudml.org/doc/210840>.

@article{Flammenkamp2000,

abstract = {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 $(2^mk)_\{m ≥ 1\}$ consists entirely of noncototients. We then use computations to detect seven such positive integers k.},

author = {Flammenkamp, A., Luca, F.},

journal = {Colloquium Mathematicae},

keywords = {Euler's function; noncototient},

language = {eng},

number = {1},

pages = {37-41},

title = {Infinite families of noncototients},

url = {http://eudml.org/doc/210840},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Flammenkamp, A.

AU - Luca, F.

TI - Infinite families of noncototients

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 1

SP - 37

EP - 41

AB - 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 $(2^mk)_{m ≥ 1}$ consists entirely of noncototients. We then use computations to detect seven such positive integers k.

LA - eng

KW - Euler's function; noncototient

UR - http://eudml.org/doc/210840

ER -

## References

top- [1] J. Browkin and A. Schinzel, On integers not of the form n-ϕ(n), Colloq. Math. 68 (1995), 55-58. Zbl0820.11003
- [2] P. Erdős, On integers of the form ${2}^{k}+p$ and related problems, Summa Brasil. Math. 2 (1950), 113-123.
- [3] R. K. Guy, Unsolved Problems in Number Theory, Springer, 1994.
- [4] H. Riesel, Nοgra stora primtal [Some large primes], Elementa 39 (1956), 258-260 (in Swedish).
- [5] W. Sierpiński, Sur un problème concernant les nombres $k\xb7{2}^{n}+1$, Elem. Math. 15 (1960), 73-74; Corrigendum, ibid. 17 (1962), 85. Zbl0093.04602
- [6] The Riesel Problem, http:/vamri.xray.ufl.edu/proths/rieselprob.html.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.