Sorry I'm dense. I understand that. But the first polynomial is not remotely related to the second other than the gcd of both is x-8. Why? On Aug 8, 2015 8:08 PM, "'Pascal Jasmin' via Programming" < [email protected]> wrote:
> (x-1)x(x+1) or x(x+1)(x+2) and their expansions are algebraic solutions to > special products. All the solutions posted used one of these 2 forms. > (your example uses the 2nd's expansion) > > > ----- Original Message ----- > From: Don Guinn <[email protected]> > To: Programming forum <[email protected]> > Cc: > Sent: Saturday, August 8, 2015 9:53 PM > Subject: Re: [Jprogramming] Detecting special products > > Using polynomials to solve this problem is really neat, but why does it > work? I can't find anything on the internet explaining why it works. > > p._720 2 3 1 > +-+----------------------------+ > |1|_5.5j7.72981 _5.5j_7.72981 8| > +-+----------------------------+ > p.1;-8 9 10 > 720 242 27 1 > > Obviously the polynomial for the roots is quite different from that used > above. There has to be a proof somewhere. > > On Fri, Aug 7, 2015 at 9:47 PM, Don Kelly <[email protected]> wrote: > > > correction : 'will be the <last> number of the sequence' > > in any case for a special number the real root will be an integer. > > > > > > On 06/08/2015 4:06 PM, Don Kelly wrote: > > > >> also try > >> 0=1|( <1; 2) {>p.|.1 3 2,-]720 > >> > >> 1_ > >> > >> 0=1|( <1; 2) {>p.|.1 3 2,-]719 > >> > >> 0 > >> > >> note that > >> (<1;2) {>p._y 2 3 1 > >> will return an integer for a special number and this will be the first > >> number of the sequence > >> based on x*x+1)*(x+2) -y=0 giving an integral root > >> p._720 2 3 1 > >> > >> ┌─┬────────────────────────────┐ > >> > >> │1│_5.5j7.72981 _5.5j_7.72981 8│ > >> > >> └─┴────────────────────────────┘ > >> > >> > >> a modification to x(x^2-1) gives an integral real root for the middle > root > >> p. _720 _1 0 1 > >> > >> ┌─┬────────────────────────────┐ > >> > >> │1│9 _4.5j7.72981 _4.5j_7.72981│ > >> > >> └─┴────────────────────────────┘ > >> > >> puts the real root first rather than last > >> > >> As for finding a list of these special numbers-the "stope " function > >> works well > >> f=:3^!.1~[:i.] > >> > >> f 10 > >> > >> 0 6 24 60 120 210 336 504 720 990 > >> > >> > >> Don Kelly > >> > >> > >> > >> > >> > >> On 06/08/2015 1:02 PM, Roger Hui wrote: > >> > >>> g=: = (^&3 - ])@:(3&(>.@%:)) > >>> g */"1 (10^40 60 80x)+/0 1 2 > >>> 1 1 1 > >>> > >>> > >>> On Thu, Aug 6, 2015 at 11:23 AM, 'Pascal Jasmin' via Programming < > >>> [email protected]> wrote: > >>> > >>> (] = (^&3 - ])@:(1r3 >.@^~ ])) 990 > >>>> > >>>> > >>>> > >>>> ----- Original Message ----- > >>>> From: Kip Murray <[email protected]> > >>>> To: "[email protected]" <[email protected]> > >>>> Cc: > >>>> Sent: Thursday, August 6, 2015 1:58 PM > >>>> Subject: [Jprogramming] Detecting special products > >>>> > >>>> The number 720 is special: it is 8*9*10 the product of three > >>>> successive non-negative integers. The first few special numbers are > >>>> > >>>> */"1 [ 0 1 2 +"1 0 i. 10 > >>>> 0 6 24 60 120 210 336 504 720 990 > >>>> > >>>> Write a verb test that tests whether a non-negative integer is > >>>> special: > >>>> > >>>> test 720 > >>>> 1 > >>>> test 0 > >>>> 1 > >>>> test 721 > >>>> 0 > >>>> > >>>> --Kip Murray > >>>> > >>>> > >>>> > >>>> -- > >>>> Sent from Gmail Mobile > >>>> ---------------------------------------------------------------------- > >>>> For information about J forums see > http://www.jsoftware.com/forums.htm > > >>>> ---------------------------------------------------------------------- > >>>> For information about J forums see > http://www.jsoftware.com/forums.htm > >>>> > >>>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > >>> > >>> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
