Permutations Destroying Arithmetic Structure
Permutations Destroying Arithmetic Structure
Given a linear form $C_1X_1 + \cdots + C_nX_n$, with coefficients in the integers, we characterize exactly the countably infinite abelian groups $G$ for which there exists a permutation $f$ that maps all solutions $(\alpha_1, \ldots , \alpha_n) \in G^n$ (with the $\alpha_i$ not all equal) to the equation $C_1X_1 …