On locally repeated values of certain arithmetic functions, I

P. Erdős, A. Sárközy, C. Pomerance

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n) = m + ν(m) has many solutions with n ≠ m. We also show that if ν is replaced by an arbitrary, integer-valued function f with certain properties assumed about its average order, then the equation n + f(n) = m + f(m) has infinitely many solutions with n ≠ m.

Original languageEnglish
Pages (from-to)319-332
Number of pages14
JournalJournal of Number Theory
Volume21
Issue number3
DOIs
Publication statusPublished - 1985

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Arithmetic Functions
Infinitely Many Solutions
Prime factor
Denote
Distinct
Integer
Arbitrary

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On locally repeated values of certain arithmetic functions, I. / Erdős, P.; Sárközy, A.; Pomerance, C.

In: Journal of Number Theory, Vol. 21, No. 3, 1985, p. 319-332.

Research output: Contribution to journalArticle

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