Re: Diophantic Equations with Constraints

*To*: mathgroup at smc.vnet.net*Subject*: [mg49495] Re: Diophantic Equations with Constraints*From*: "Dana DeLouis" <delouis at bellsouth.net>*Date*: Thu, 22 Jul 2004 02:45:06 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Just a quick and dirty way to test if there is a possibility of a solution (maybe not integer) might be something like this. The solution is in the range of 0-47, so we can quickly see that with 148, there are no solutions. However, 14 is in the range, so there is a "chance" there might be integer solutions. In[1]:= 3*x + 2*y - z /. {x -> Interval[{3, 8}], y -> Interval[{0, 12}], z -> Interval[{1, 9}]} Out[1]= Interval[{0, 47}] In[2]:= FindInstance[ {3*x + 2*y - z == 14, 3 <= x <= 8, 0 <= y <= 12, 1 <= z <= 9}, {x, y, z}, Integers, 100]