In this paper, we mainly answer a Lampe's question [3] about the solutions of a Diophantine equation, that is, we give a criterion to determine which solutions of the Diophantine equation are in the orbit of the initial solution (ϵ,ϵ,ϵ,ϵ,ϵ) under the actions of the group G which is defined by mutations of a cluster algebra. In order to do this, using a rational map φ, we transform the Diophantine equation to a related equation whose all positive integral solutions form the orbit of an initial solution φ(ϵ,ϵ,ϵ,ϵ,ϵ)=(3,4,4) under the actions of the group G˜, and the set S(3,4,4) is shown to be the orbit of (ϵ,ϵ,ϵ,ϵ,ϵ) under the actions of a subgroup of G. Then the criterion is proved as the main conclusion.