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Solving equations and inequalities with Reduce - how?

• To: mathgroup at smc.vnet.net
• Subject: [mg87655] Solving equations and inequalities with Reduce - how?
• From: Marc Heusser <marc.heusser at byeheusser.commercialspammers.invalid>
• Date: Tue, 15 Apr 2008 05:50:04 -0400 (EDT)
• Organization: University of Zurich

I tried to solve equations with Reduce and somehow did not quite 
formulate it right, so Reduce complains with 
"Reduce::ivar: 1 is not a valid variable".

This is what I tried:

Wanted: A six digit number satisfying the following conditions:
The first digit is not zero.
If you take the first two digits and move them to the end of the number, 
the resulting number must be twice the original number.

In[23]:=Reduce[200000a +20000 b +2000 c+200 d+20 e  +       2 f 
\[Equal]100000c +10000 d +1000 e+100 f+10 a  + b ,  {a,b,c,d,e,f}, 
Modulus\[Rule]9]

I did solve the problem through exhaustive search:

In[14]:=Timing[Select[Range[10^6],    FractionalPart[#/10000] 1000000 + 
IntegerPart[#/10000]\[Equal] 2  #&]]
Out[14]={34.2848 Second,{142857,285714,428571}}

but would like to understand how to use Reduce (or another function) to 
solve such a set of equations.

TIA

Marc

-- 
remove bye and from mercial to get valid e-mail
<http://www.heusser.com>

• Follow-Ups:
  • Re: Solving equations and inequalities with Reduce - how?
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Solving equations and inequalities with Reduce - how?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Solving equations and inequalities with Reduce - how?
    • From: "W_Craig Carter" <ccarter@mit.edu>