Re: Diophantic equations

• To: mathgroup at smc.vnet.net
• Subject: [mg32769] Re: [mg32746] Diophantic equations
• From: BobHanlon at aol.com
• Date: Sat, 9 Feb 2002 05:11:39 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2/8/02 4:22:23 AM, ulbrich at biochem.mpg.de writes:

>I try to solve equations where only integers are allowed, like
>
>a + b + 10 c = 100
>5 a + 2 b + c = 100
>
>a, b, c should be integers and positve.
>
>How can I do this?

Using brute force

Needs["Algebra`InequalitySolve`"];

var = {a,b,c};
]
eqn={a+b+10 c==100,5 a+2 b+c==100};

ineqEqn = (eqn /. Equal -> LessEqual)

{a + b + 10*c <= 100, 5*a + 2*b + c <= 100}

rng = Sort[((InequalitySolve[ineqEqn /.

{#[[1]]->1,#[[2]]->1}, #[[3]]] /.

x_?NumberQ -> Floor[x])& /@

NestList[RotateLeft[#,1]& , var, 2])] /.

LessEqual[x_,y_] :> Range[1,y];

Select[Flatten[Outer[List,Sequence@@rng], 2],

{{a -> 11, b -> 19, c -> 7}}

eqn /. soln

{{True, True}}

Bob Hanlon
Chantilly, VA  USA

```

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