       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

```

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