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?
>

```

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