OK, rereading the original post, I guess I should assume that we are not only interested in the decimal case.
That said, I'm not certain that it makes sense to assume that the least common denominator has been factored out of p and q, either. -- Raul On Jul 23, 2014 1:28 AM, "greg heil" <[email protected]> wrote: > Raul > > >Well the way i read Dans query only q and b are important... so if > bq=:([:q:])-.([:q:[) > then a null result would be finite, eg > 3 bq 3 > 10 bq 3 > 3 > > greg > ~krsnadas.org > > -- > > from: Raul Miller <[email protected]> > reply-to: [email protected] > to: Chat forum <[email protected]> > date: 22 July 2014 20:42 > subject: Re: [Jchat] Repeating decimals > > That's an interesting point. > > >Nevertheless, given the subject line of this thread, I think that maybe > the base has already been determined. > > Thanks, > > -- > Raul > > -- > > from: greg heil <[email protected]> > to: Chat forum <[email protected]> > date: 22 July 2014 19:42 > subject: Re: [Jchat] Repeating decimals > > >What ever formula would also depend on b ... eg the division of 1 by 3 > has a finite representation in base 3 of 0.1. (although its representation > in base 10 is infinite) > > greg > ~krsnadas.org > > -- > > from: Raul Miller <[email protected]> > to: Chat forum <[email protected]> > date: 22 July 2014 10:18 > subject: Re: [Jchat] Repeating decimals > > $p(2 5-.~[:q:]%+.)q > 0 > > >Assuming p and q are rank 0, of course. (And this is a reasonable > assumption, since the problem statement suggests no use for dimensions). > > Thanks, > > -- > Raul > > -- > > from: Dan Bron <[email protected]> > to: [email protected] > date: 22 July 2014 08:25 > subject: [Jchat] Repeating decimals > > >Given 3 positive integers p,q and b, where p and q represent the > numerator and denominator of a rational number (respectively), and b a > numerical base (or radix), how can we know if p%q has a finite (or not) > representation in b? > > >In other words, if p%q can be represented by a finite > (non-infinitely-repeating) decimal in base b, then what do we know about > the relationship of p to q or p%q to b ? > > >You may allow p to take on the value 0 if needed for generality, but q is > strictly > 0 (obviously) and b is strictly > 1 (probably?). > > -Dan > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
