On locally repeated values of certain arithmetic functions,I |
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Authors: | P Erdös A Sárközy C Pomerance |
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Institution: | Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary;Department of Mathematics, University of Georgia, Athens, Georgia 30602 USA |
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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. |
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