# On integers not of the form n - φ (n)

Colloquium Mathematicae (1995)

- Volume: 68, Issue: 1, page 55-58
- ISSN: 0010-1354

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topBrowkin, J., and Schinzel, A.. "On integers not of the form n - φ (n)." Colloquium Mathematicae 68.1 (1995): 55-58. <http://eudml.org/doc/210293>.

@article{Browkin1995,

abstract = {W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^k·509203$ (k = 1, 2,...) is of the form n - φ(n).},

author = {Browkin, J., Schinzel, A.},

journal = {Colloquium Mathematicae},

keywords = {Sierpiński problem; Euler phi-function; open problem},

language = {eng},

number = {1},

pages = {55-58},

title = {On integers not of the form n - φ (n)},

url = {http://eudml.org/doc/210293},

volume = {68},

year = {1995},

}

TY - JOUR

AU - Browkin, J.

AU - Schinzel, A.

TI - On integers not of the form n - φ (n)

JO - Colloquium Mathematicae

PY - 1995

VL - 68

IS - 1

SP - 55

EP - 58

AB - W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^k·509203$ (k = 1, 2,...) is of the form n - φ(n).

LA - eng

KW - Sierpiński problem; Euler phi-function; open problem

UR - http://eudml.org/doc/210293

ER -

## References

top- [1] A. Aigner, Folgen der Art $a{r}^{n}+b$, welche nur teilbare Zahlen liefern, Math. Nachr. 23 (1961), 259-264. Zbl0100.26904
- [2] P. Erdős, Über die Zahlen der Form σ(n)-n und n-φ(n), Elem. Math. 28 (1973), 83-86.
- [3] W. Keller, Woher kommen die größ ten derzeit bekannten Primzahlen?, Mitt. Math. Ges. Hamburg 12 (1991), 211-229.
- [4] W. Sierpiński, Number Theory, Part II, PWN, Warszawa, 1959 (in Polish).

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