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- W2004671930 abstract "Let m and n be positive integers, and let f ( n ) be an arithmetic function. We discuss subsets E of the set of positive integers, for which f ( m + n ) = f ( m ) + f ( n ) whenever m , n ∈ E . (The set E need not be maximal for f .) Our main result is that if f is multiplicative, there is a nonsquarefull integer m with f ( m ) ≠ 0, and E is the set of primes, then we have f ( n ) = n for all n . The proof uses results on the set of exceptions to Goldbach's Conjecture. We examine related problems, including some density questions." @default.
- W2004671930 created "2016-06-24" @default.
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- W2004671930 date "1992-10-01" @default.
- W2004671930 modified "2023-10-16" @default.
- W2004671930 title "Additive uniqueness sets for arithmetic functions" @default.
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- W2004671930 doi "https://doi.org/10.1016/0022-314x(92)90022-h" @default.
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