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On locally repeated values of certain arithmetic functions, I (1985)
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by
P. Erdős
,
A. Sarközy
,
C. Pomerance
| Citations: | 7 - 2 self |
BibTeX
@MISC{Erdős85onlocally,
author = {P. Erdős and A. Sarközy and C. Pomerance},
title = {On locally repeated values of certain arithmetic functions, I},
year = {1985}
}
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Abstract
Let v(n) denote the number of distinct prime factors of n. We show that the equation n + v(n) = m + v(m) has many solutions with n #M. We also show that if v 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.
