Consider the complex numbers C as a module over integers Z, and let a be a complex number.
Consider the subset W_a = {1,a,a^2,...,a^n,...}
of the Z-module C. Then I want to show that
W_a is linearly independent iff a is a transcedent number.
Consider the complex numbers C as a module over integers Z, and let a be a complex number.
Consider the subset W_a = {1,a,a^2,...,a^n,...}
of the Z-module C. Then I want to show that
W_a is linearly independent iff a is a transcedent number.