Abstract
Let x1,...,xr be complex numbers with K = Q(x1,...,xr) having transcendence degree r-1 over Q. Consider the equation
a1x1+...+akxk = 1, (1)
in which the ai's are fixed elements of K×, no proper subsum ai1xi1+...+aijxij vanishes, and we seek solutions xi Î G = . It is well-known that (1) has only finitely many solutions; we present here an elementary proof of this fact using results from the entropy theory of commuting group automorphisms.
Original language | English |
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Pages (from-to) | 137-143 |
Number of pages | 7 |
Journal | Journal of Number Theory |
Volume | 53 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1995 |