Re: modulo solving lacking domain?

*To*: mathgroup at smc.vnet.net*Subject*: [mg126851] Re: modulo solving lacking domain?*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Wed, 13 Jun 2012 04:56:37 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201206120659.CAA25892@smc.vnet.net>

On 12 Jun 2012, at 07:59, Richard Fateman wrote: > Solve[12*n==8,n,Modulus->20] > > returns > {{n->4+5*C[1]}} > > It omits C[1] element of Integers. > I doubt that this is a feature; is it a bug? > > C[1] is not necessarily a member of the finite field of > integers modulo 20. It is obvious not an arbitrary Real. > Integers modulo 20 do not form a finite field. Since 4*5 = 0 modulo 20, so 4 and 5 are zero divisors modulo 20 Integers modulo 20 do are not even an integral domain. The constant in the answer is obviously an integer modulo 20. Probably a mariginally better answer would be {{n->ConditionalExpression[4+5 C[1],Element[C[1],Integers]}} Andrzej Kozlowski

**References**:**modulo solving lacking domain?***From:*Richard Fateman <fateman@cs.berkeley.edu>