A Uniqueness Theorem for Rational Points in Projective Space Original Research Article

This paper proves a uniqueness result of the following type which has an analogy in Nevanlinna theory. Let K be a number field and S a finite set of places of K containing the infinite places. Let L1, …, L3m+2 be linear forms in m+1 variables with coefficients in image which are in general position. Let xn, yn be two infinite sequences in imagem(K) such that at least one of them is non-degenerate and such that Lj(xn)≠0, Lj(yn)≠0, and Lj(xn)/Lj(yn) is an S-unit for 1less-than-or-equals, slantjless-than-or-equals, slant3m+2. Then there exists an infinite subsequence {nk} with xnk=ynk.