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摘要
We prove a strong form of the "n Squares Problem" over polynomial rings with characteristic zero constant field. In particular we prove: for all r >= 2 there exists an integer M = M(r) depending only on r such that, if z(1), z(2), ..., z(M) are M distinct elements of F and we have polynomials f,g,x(1),x(2) ..., x(M) is an element of F[t] with some xi non-constant, satisfiying the equations x(i)(r) = (z(i) + f)(r) + g for each i, then g is the zero polynomial.
- 出版日期2010-5
