Re: Diophantic Equations with Constraints

*To*: mathgroup at smc.vnet.net*Subject*: [mg49456] Re: [mg49443] Diophantic Equations with Constraints*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 21 Jul 2004 06:39:16 -0400 (EDT)*References*: <200407201153.HAA23709@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 20 Jul 2004, at 20:53, Michael S. wrote: > *This message was transferred with a trial version of CommuniGate(tm) > Pro* > Hi group, > > given an equation like > > 3x + 2y - z == 148 > with > x in Range[3,8], > y in Range[0,12], > z in Range[1,9], > > what would be the best way to solve this? > > Thanks and best regards, > > Michael > > Trying the simplest way: Reduce[{3*x + 2*y - z == 148, 3 <= x <= 8, 0 <= y <= 12, 1 <= z <= 9}, {x, y, z}, Integers] False No solutions. Just to confirm this here is another approach: NMinimize[{Abs[3*x + 2*y - z - 148], 3 <= x <= 8 && 0 <= y <= 12 && 1 <= z <= 9 && (x | y | z) $B":(B Integers}, {x, y, z}] {101., {x -> 8, y -> 12, z -> 1}} Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Diophantic Equations with Constraints***From:*"Michael S." <MikeSuesserott@t-online.de>