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Math brain teaser
12-29-2013, 08:33 AM
Post: #25
RE: Math brain teaser
(12-27-2013 05:18 AM)Han Wrote:  A computer generates a random polynomial whose coefficients are non-negative integers.
(12-29-2013 01:46 AM)Les_Koller Wrote:  Say you choose just pi. If our polynomial is p(x) = x we get pi. If our polynomial is p(x) = pi, then we also get pi, thus not identifying the polynomial completely.
That can not be: \(p(x)=\pi\) doesn't have coefficients that are non-negative integers. \(\pi\) isn't an integer.
OTOH: if \(p(\pi)=q(\pi)\) for some distinct polynomials \(p(x)\) and \(q(x)\) then \(p(\pi)-q(\pi)=0\).
But \(\pi\) can't be the root of a polynomial with integer coefficients since it's transcendent.
Thus you can distinguish these kind of polynomials based on the evaluation at \(\pi\). Or any other transcendent number.

Cheers
Thomas
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Messages In This Thread
Math brain teaser - Han - 12-27-2013, 05:18 AM
RE: Math brain teaser - Les_Koller - 12-27-2013, 05:54 AM
RE: Math brain teaser - Les_Koller - 12-27-2013, 07:41 AM
RE: Math brain teaser - Namir - 12-27-2013, 01:24 PM
RE: Math brain teaser - Han - 12-27-2013, 05:29 PM
RE: Math brain teaser - Thomas Klemm - 12-27-2013, 05:56 PM
RE: Math brain teaser - Han - 12-27-2013, 06:13 PM
RE: Math brain teaser - Namir - 12-27-2013, 10:02 PM
RE: Math brain teaser - Paul Dale - 12-27-2013, 10:52 PM
RE: Math brain teaser - Thomas Klemm - 12-28-2013, 11:20 AM
RE: Math brain teaser - Han - 12-27-2013, 11:00 PM
RE: Math brain teaser - Les_Koller - 12-28-2013, 02:03 AM
RE: Math brain teaser - Paul Dale - 12-28-2013, 02:45 AM
RE: Math brain teaser - walter b - 12-28-2013, 04:31 AM
RE: Math brain teaser - Thomas Klemm - 12-28-2013, 11:11 AM
RE: Math brain teaser - walter b - 12-28-2013, 12:17 PM
RE: Math brain teaser - Thomas Klemm - 12-28-2013, 12:55 PM
RE: Math brain teaser - Paul Dale - 12-28-2013, 11:58 AM
RE: Math brain teaser - Les_Koller - 12-28-2013, 09:21 PM
RE: Math brain teaser - Thomas Klemm - 12-29-2013, 12:10 AM
RE: Math brain teaser - Les_Koller - 12-29-2013, 01:46 AM
RE: Math brain teaser - Thomas Klemm - 12-29-2013 08:33 AM
RE: Math brain teaser - Les_Koller - 12-29-2013, 01:50 AM
RE: Math brain teaser - Paul Dale - 12-29-2013, 01:54 AM
RE: Math brain teaser - Thomas Klemm - 12-29-2013, 11:25 AM
RE: Math brain teaser - Les_Koller - 12-29-2013, 01:58 AM
RE: Math brain teaser - Les_Koller - 12-29-2013, 05:52 PM



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