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MathGroup Archive 2002

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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];

soln = Thread[var->#]& /@
 
    Select[Flatten[Outer[List,Sequence@@rng], 2],
 
      And@@(eqn /. Thread[var->#])&]

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

eqn /. soln

{{True, True}}


Bob Hanlon
Chantilly, VA  USA


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