Multiplicative dependence of the translations of algebraic numbers
Multiplicative dependence of the translations of algebraic numbers
In this paper, we first prove that given pairwise distinct algebraic numbers \alpha_1, \ldots, \alpha_n , the numbers \alpha_1+t, \ldots, \alpha_n+t are multiplicatively independent for all sufficiently large integers t . Then, for a pair (a,b) of distinct integers, we study how many pairs (a+t,b+t) are multiplicatively dependent when t …