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On the functional
equation F(mn)F((m,
n)) = F(m)F(n)f((m,n))
James E. Shockley |
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Vol. 18 (1966), No. 1, 185–189
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Abstract |
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Let f be a multiplicative arithmetic function, f(1) = 1. Necessary and sufficient conditions on f will be found so that the functional equation  will have a solution F with F(1)≠0 and all solution F will be determined. It will be shown that two different types of solutions may exist and that one of these requires that f have a property similar to complete multiplicativity. |
Mathematical Subject Classification
Primary: 10.43
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Milestones
Received: 23 October 1964
Revised: 24 February 1965
Published: 1 July 1966
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Authors |
| James E. Shockley | |
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