Additive uniqueness of PRIMES − 1 for multiplicative functions
2020 ◽
Vol 16
(06)
◽
pp. 1369-1376
Keyword(s):
Let [Formula: see text] be the set of all primes. A function [Formula: see text] is called multiplicative if [Formula: see text] and [Formula: see text] when [Formula: see text]. We show that a multiplicative function [Formula: see text] which satisfies [Formula: see text] satisfies one of the following: (1) [Formula: see text] is the identity function, (2) [Formula: see text] is the constant function with [Formula: see text], (3) [Formula: see text] for [Formula: see text] unless [Formula: see text] is odd and squareful. As a consequence, a multiplicative function which satisfies [Formula: see text] is the identity function.
2018 ◽
Vol 14
(02)
◽
pp. 469-478
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Keyword(s):
1996 ◽
Vol 19
(2)
◽
pp. 209-217
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2017 ◽
Vol 153
(8)
◽
pp. 1622-1657
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2017 ◽
Vol 148
(1)
◽
pp. 63-77
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2003 ◽
Vol 2003
(37)
◽
pp. 2335-2344
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2018 ◽
Vol 2020
(5)
◽
pp. 1300-1345
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Keyword(s):