FindInstance over Integers

*To*: mathgroup at smc.vnet.net*Subject*: [mg101077] FindInstance over Integers*From*: "zac.ernst" <zac.ernst at gmail.com>*Date*: Tue, 23 Jun 2009 07:07:11 -0400 (EDT)

Hello -- I'm working on a project which requires the program to determine whether a given set of equalities and inequalities is satisfiable over the integers. Of course, this problem is not decidable in general. But I just need a "good enough" function that will at least report that a set of constraints is satisfiable only if it actually is, and work across some fairly easy cases. FindInstance is the obvious function to use, but it seems to fail for constraints that are very easy to satisfy. The simplest example I can come up with is this: FindInstance[x == 2^y && x > 2, {x, y}, Integers] Clearly, {x->4, y->2} would satisfy these constraints, but Mathematica reports that "the methods available to FindInstance are insufficient...". It may be relevant that if I change "x > 2" to "x > 1", then Mathematica has no problem finding a solution. Are there any workarounds or alternatives to this approach? Thanks very much, -Zac

**Follow-Ups**:**Re: FindInstance over Integers***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>