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In this paper the general translation equation on an arbitrary n-group is considered, namely the equation of the form varphi(varphi(varphi(... varphi(varphi(α, x1), x2), ...), xn-1), xn = varphi(α, [x1, x2, ..., xn]), where Γ is a set, (G, [...]) is an n-group and varphi: Γ x G → Γ. There are proved two theorems giving a characterization of the solutions of the above-mentioned equation by the solutions...
The following three types of functional equations connected with translation equation are considered: equations reducible to that equation; those with a solution of the translation equation occurring in the equation and ones which are implied by the translation equation. The stability problem for translation equation is also dealt with.
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