On linear functional equations modulo Z.

In this paper, we consider the condition ∑ i = 0 n + 1 φ i (r i x + q i y) ∈ Z for real valued functions defined on a linear space V. We derive necessary and sufficient conditions for functions satisfying this condition to be decent in the following sense: there exist functions f i : V → R , g i : V → Z such that φ i = f i + g i , (i = 0 , ⋯ , n + 1) and ∑ i = 0 n + 1 f i (r i x + q i y) = 0 for all x , y ∈ V . [ABSTRACT FROM AUTHOR]