### 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 |
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Pages (from-to) | 319-332 |

Number of pages | 14 |

Journal | Journal of Number Theory |

Volume | 21 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*21*(3), 319-332. https://doi.org/10.1016/0022-314X(85)90059-9

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

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 21, no. 3, pp. 319-332. https://doi.org/10.1016/0022-314X(85)90059-9

}

TY - JOUR

T1 - On locally repeated values of certain arithmetic functions, I

AU - Erdős, P.

AU - Sárközy, A.

AU - Pomerance, C.

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33751166766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751166766&partnerID=8YFLogxK

U2 - 10.1016/0022-314X(85)90059-9

DO - 10.1016/0022-314X(85)90059-9

M3 - Article

AN - SCOPUS:33751166766

VL - 21

SP - 319

EP - 332

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 3

ER -