Re: Solving equations and inequalities with Reduce - how?

*To*: mathgroup at smc.vnet.net*Subject*: [mg87710] Re: [mg87655] Solving equations and inequalities with Reduce - how?*From*: "W_Craig Carter" <ccarter at mit.edu>*Date*: Wed, 16 Apr 2008 05:00:33 -0400 (EDT)*References*: <200804150950.FAA24909@smc.vnet.net>

Hello Marc, Your initial example worked fine for me: Reduce[200000 a + 20000 b + 2000 c + 200 d + 20 e + 2 f == 100000 c + 10000 d + 1000 e + 100 f + 10 a + b, {a, b, c, d, e, f}, Modulus -> 9] resulted in a == C[1] && b == C[2] && c == C[3] && d == C[4] && e == C[5] && f == 8 C[1] + 8 C[2] + 8 C[3] + 8 C[4] + 8 C[5] Perhaps you had a typo? In your original post you had 20000a and not 20000 a Craig On Tue, Apr 15, 2008 at 5:50 AM, Marc Heusser <marc.heusser at byeheusser.commercialspammers.invalid> wrote: > 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> > > -- W. Craig Carter

**References**:**Solving equations and inequalities with Reduce - how?***From:*Marc Heusser <marc.heusser@byeheusser.commercialspammers.invalid>