科研之友
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摘要
In this article, we consider the problem on finding non-degenerate n-ary m-ic forms having an n x n matrix A as a linear isomorphism. We show that it is equivalent to solve a linear diophantine equation. In particular, we find all integral ternary cubic forms having A as a linear isomorphism, for any A is an element of GL(3) (Z). We also give a family of non-degenerate cubic forms F such that F(x) = N always has infinitely many integer solutions if exists.
- 出版日期2016-11
