       RE: Diophantic Equations with Constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg49483] RE: [mg49443] Diophantic Equations with Constraints
• From: "Florian Jaccard" <florian.jaccard at eiaj.ch>
• Date: Thu, 22 Jul 2004 02:44:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello !

You can use Reduce :

In:=
Reduce[3*x + 2*y - z == 14 && 3 <= x <= 8 &&
0 <= y <= 12 && 1 <= z <= 9, {x, y, z}, Integers]

Out=
y == 0 && z == 1 && x == 5 || y == 0 && z == 4 &&
x == 6 || y == 0 && z == 7 && x == 7 ||
y == 1 && z == 3 && x == 5 || y == 1 && z == 6 &&
x == 6 || y == 1 && z == 9 && x == 7 ||
y == 2 && z == 2 && x == 4 || y == 2 && z == 5 &&
x == 5 || y == 2 && z == 8 && x == 6 ||
y == 3 && z == 1 && x == 3 || y == 3 && z == 4 &&
x == 4 || y == 3 && z == 7 && x == 5 ||
y == 4 && z == 3 && x == 3 || y == 4 && z == 6 &&
x == 4 || y == 4 && z == 9 && x == 5 ||
y == 5 && z == 5 && x == 3 || y == 5 && z == 8 &&
x == 4 || y == 6 && z == 7 && x == 3 ||
y == 7 && z == 9 && x == 3

Greetings

F.Jaccard

-----Message d'origine-----
De : Michael S. [mailto:MikeSuesserott at t-online.de]
Envoyé : mar., 20. juillet 2004 13:54
À : mathgroup at smc.vnet.net
Objet : [mg49443] Diophantic Equations with Constraints

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

```

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