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Re: modulo solving lacking domain?

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

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