# On locally repeated values of certain arithmetic functions, I

P. Erdős, A. Sárközy, C. Pomerance

Research output: Article

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 language English 319-332 14 Journal of Number Theory 21 3 https://doi.org/10.1016/0022-314X(85)90059-9 Published - 1985

### Fingerprint

Arithmetic Functions
Infinitely Many Solutions
Prime factor
Denote
Distinct
Integer
Arbitrary

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

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

Research output: Article

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AU - Sárközy, A.

AU - Pomerance, C.

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