Solutions of the Functional Equation (f(x))2 - f(x2) = h(x)
Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 113-120

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In a recent paper [2] Lambek and Moser have introduced the functional equations 1 and 2 in connection with some problems of number theory, in particular in dealing with the sums by pairs of sets of integers. The second may be put into the same form as (1) by the substitutions x = In z, f(ln z) = F(z), h(ln z) = H(z).
Baker, I. N. Solutions of the Functional Equation (f(x))2 - f(x2) = h(x). Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 113-120. doi: 10.4153/CMB-1960-012-8
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     author = {Baker, I. N.},
     title = {Solutions of the {Functional} {Equation} (f(x))2 - f(x2) = h(x)},
     journal = {Canadian mathematical bulletin},
     pages = {113--120},
     year = {1960},
     volume = {3},
     number = {2},
     doi = {10.4153/CMB-1960-012-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1960-012-8/}
}
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