Kurepa's functional equation on semigroups.
Stochastica, Tome 6 (1982) no. 1, p. 39.

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The functional equation to which the title refers is:F(x,y) + F(xy,z) = F(x,yz) + F(y,z),where x, y and z are in a commutative semigroup S and F: S x S --> X with (X,+) a divisible abelian group (Divisibility means that for any y belonging to X and natural number n there exists a (unique) solution x belonging to X to nx = y).
Classification : 91B16, 20M15, 39B52, 39B99
Mots-clés : Ecuaciones funcionales, Grupos, Kurepa's functional equation, commutative semigroup, divisible Abelian group, Gaussian semigroup 
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     author = {Bruce R. Ebanks},
     title = {Kurepa's functional equation on semigroups.},
     journal = {Stochastica},
     pages = {39},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {1982},
     mrnumber = {MR0694203},
     zbl = {0524.39010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/STO_1982__6_1_38865/}
}
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Bruce R. Ebanks. Kurepa's functional equation on semigroups.. Stochastica, Tome 6 (1982) no. 1, p. 39. https://geodesic-test.mathdoc.fr/item/STO_1982__6_1_38865/