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A note on the Levi-Civita functional equation

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In this paper we find the solutions of the functional equation

$$\begin{aligned} f(xy)=g(x)h(y)+\sum _{j=1}^{n}g_j(x)h_j(y),\;x,y \in M, \end{aligned}$$

where M is a monoid, \(n\ge 2\), and \(g_j\) (for \(j=1,\ldots ,n\)) are linear combinations of at least 2 distinct nonzero multiplicative functions.

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Correspondence to Elhoucien Elqorachi.

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Belfakih, K., Elqorachi, E. A note on the Levi-Civita functional equation. Aequat. Math. 93, 1275–1291 (2019).

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