       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/

```

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