On integers not of the form n - φ (n)

Browkin, J.; Schinzel, A.

Colloquium Mathematicae, Tome 68 (1995), p. 55-58 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $2^{k} \cdot 509203$ (k = 1, 2,...) is of the form n - φ(n).

Publié le : 1995-01-01

Zbl 0820.11003

EUDML-ID : urn:eudml:doc:210293

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     author = {J. Browkin and A. Schinzel},
     title = {On integers not of the form n - $\phi$ (n)},
     journal = {Colloquium Mathematicae},
     volume = {68},
     year = {1995},
     pages = {55-58},
     zbl = {0820.11003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p55bwm}
}

Browkin, J.; Schinzel, A. On integers not of the form n - φ (n). Colloquium Mathematicae, Tome 68 (1995) pp. 55-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p55bwm/

Bibliographie

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[001] [2] P. Erdős, Über die Zahlen der Form σ(n)-n und n-φ(n), Elem. Math. 28 (1973), 83-86.

[002] [3] W. Keller, Woher kommen die größ ten derzeit bekannten Primzahlen?, Mitt. Math. Ges. Hamburg 12 (1991), 211-229.

[003] [4] W. Sierpiński, Number Theory, Part II, PWN, Warszawa, 1959 (in Polish).