most recent 30 from http://mathoverflow.net 2013-05-23T00:07:45Z http://mathoverflow.net/feeds/user/9002 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37673/on-special-type-polynomial-inequalities-over-integers Bakh 2010-09-03T23:04:04Z 2010-09-04T14:17:36Z

<p>A special monomial is a monomial of the form $C\cdot x_{i_1} \cdot \ldots \cdot x_{i_n}$, where C is an integer and no variable is repeated more than once in the monomial. For instance, $x\cdot y\cdot z\cdot u\cdot w$ is special while $x\cdot y\cdot z\cdot u\cdot w\cdot z$ is not since z is repeated. A special polynomial is a sum of special monomials. The question is the following. Is there an algorithm, that given a system of finite set of in-equations with special polynomials, decides if the system has integer solution?</p>

http://mathoverflow.net/questions/37673/on-special-type-polynomial-inequalities-over-integers/37674#37674 Bakh 2010-09-04T23:37:28Z 2010-09-04T23:37:28Z

by in-equations i meant expressions of the type $p\leq q$, where $p$ and $q$ are special polynomials. David's answer does the job. Thanks. Mark is also right that any finite set of non-equalities (expressions of the type $p\neq 0$) has an integer solution.