Re: Diophantic Equations with Constraints

*To*: mathgroup at smc.vnet.net*Subject*: [mg49476] Re: Diophantic Equations with Constraints*From*: BobHanlon at aol.com*Date*: Wed, 21 Jul 2004 06:40:12 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Using brute force (not recommended): Select[ Flatten[ Table[ {x,y,z}, {x,3,8},{y,0,12},{z,1,9}], 2], (3*#[[1]]+2*#[[2]]-#[[3]]==14&)] {{3, 3, 1}, {3, 4, 3}, {3, 5, 5}, {3, 6, 7}, {3, 7, 9}, {4, 2, 2}, {4, 3, 4}, {4, 4, 6}, {4, 5, 8}, {5, 0, 1}, {5, 1, 3}, {5, 2, 5}, {5, 3, 7}, {5, 4, 9}, {6, 0, 4}, {6, 1, 6}, {6, 2, 8}, {7, 0, 7}, {7, 1, 9}} Using Reduce over the domain Integers: % == ({x,y,z} /. {ToRules[ Reduce[ {3x+2y-z==14, 3<=x<=8,0<=y<=12,1<=z<=9},{x,y,z}, Integers]]} // Sort) True Bob Hanlon > In a message dated Tue, 20 Jul 2004 12:06:58 +0000 (UTC), < > MikeSuesserott at t-online.de> writes: 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? >