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MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
tthsqe wrote:
There are lots of integer-valued polynomials that satisfy
f(6061) = 4152
f(8016) = -1092
f(9608) = 1512
but I have no idea what the minimum degree such polynomials is.
It cannot be 0 degree or 1 degree for obvious reason - those values don't belong to the straight line. It has to be at least 2 degree polynomial. As you have seen above in my example the degree of 3 is fairly enough.
10 Jan 2014, 22:03
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
alessandro95:
nono, there is no guarantee that the lagrange polynomial though n points is integer-valued on all integers. This integer-valuedness condition is what makes the problem interesting.

MHajduk,
yes, infact my current bound on the min degree is
Code:
2 < min degree <= 9608-6061

but in order to verify your claim about degree 3, you have to produce a polynomial f(x) of degree 3 that passes through the three given points and is an integer for any integer value of x. In fact, there is no such degree 3 polynomial.

Last edited by tthsqe on 10 Jan 2014, 22:16; edited 2 times in total
10 Jan 2014, 22:04
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
[...]

Last edited by MHajduk on 10 Jan 2014, 22:37; edited 1 time in total
10 Jan 2014, 22:10
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
There is no polynomial of infinite degree - why not just take f(x) = a for that example?
I have just stated that there is a polynomial of degree 9608-6061 that does satisfy all of our conditions. The question is if you can find a polynomial of smaller degree that also satisfies of all of the conditions.
10 Jan 2014, 22:15
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
tthsqe wrote:
but in order to verify your claim about degree 3, you have to produce a polynomial f(x) of degree 3 that passes through the three given points and is an integer for any integer value of x.
I didn't claim, as I mentioned before, that my polynomial will we integer-valued for all integers but only for the given ones (and I don't expect more).
10 Jan 2014, 22:15
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
tthsqe wrote:
There is no polynomial of infinite degree
I understand that "power series" sounds better here.
10 Jan 2014, 22:19
alessandro95

Joined: 24 Mar 2013
Posts: 62
alessandro95
MHajduk wrote:
tthsqe wrote:
but in order to verify your claim about degree 3, you have to produce a polynomial f(x) of degree 3 that passes through the three given points and is an integer for any integer value of x.
I didn't claim, as I mentioned before, that my polynomial will we integer-valued for all integers but only for the given ones (and I don't expect more).

You didn't, and the polynomial I posted in the previous page should satisfy you, but tthsqe wanted a polynomial that is integer valued for every integer, but I have no idea on how to build one
10 Jan 2014, 22:22
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
alessandro95 wrote:
MHajduk wrote:
tthsqe wrote:
but in order to verify your claim about degree 3, you have to produce a polynomial f(x) of degree 3 that passes through the three given points and is an integer for any integer value of x.
I didn't claim, as I mentioned before, that my polynomial will we integer-valued for all integers but only for the given ones (and I don't expect more).

You didn't, and the polynomial I posted in the previous page should satisfy you, but tthsqe wanted a polynomial that is integer valued for every integer, but I have no idea on how to build one
Your example satisfied me as much as mine (if you cared to read what I wrote on the previous page you should know what I'm talking about). Both polynomials are of degree 3.
10 Jan 2014, 22:29
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
alessandro95, I'll let you think about how to build such polynomials and get the degree bound 3547. btw, how is your chess engine coming along?
10 Jan 2014, 22:36
HaHaAnonymous

Joined: 02 Dec 2012
Posts: 1180
Location: Unknown
HaHaAnonymous
[ Post removed by author. ]

Last edited by HaHaAnonymous on 28 Feb 2015, 18:33; edited 1 time in total
11 Jan 2014, 00:56
sleepsleep

Joined: 05 Oct 2006
Posts: 8902
Location: ˛　　　　　　　　　　　　　　　　　　　　　　　　　　　　　⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
sleepsleep
i just thought of this,
if i could let say give a set of numbers, ten thousand of 4 digits (from lottery) numbers from each week draw, could i predict the next first prize number through maths?

or could maths forms formula or relationship on ten thousand of 4 digits numbers?
13 Jan 2014, 15:27
HaHaAnonymous

Joined: 02 Dec 2012
Posts: 1180
Location: Unknown
HaHaAnonymous
[ Post removed by author. ]

Last edited by HaHaAnonymous on 28 Feb 2015, 18:33; edited 2 times in total
13 Jan 2014, 15:30
AsmGuru62

Joined: 28 Jan 2004
Posts: 1409
AsmGuru62
Lottery is unpredictable with any math.
Otherwise, it is not profitable business.

I run 10,000 lottery sets (7 out of 49) every week (based on Mersenne Twister) and
I never got anything significant, no matter what I do:

1. Sum of numbers must fall in some range
2. Exclude last week numbers from the sets
3. Previous weeks statistics...
etc. -- there are a lot of articles on the Web about "winning" the lottery,
but none of them worked.

Doing this for almost 2 years now -- nothing.
I guess, I am not as lucky as other guys.
13 Jan 2014, 15:39
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
sleepsleep. do you sign up for determinism? If so, you should be able to believe that if you knew the position of every elementary particle in the lottery machine, then the numbers it will pick are knowable in some sense. However, I agree that the numbers picked from previous weeks won't help you out here.

Also, don't play the lottery. It has been said that it is a tax on the mathematically ignorant.
13 Jan 2014, 15:52
whakamaru

Joined: 03 Oct 2012
Posts: 20
Location: New Zealand
whakamaru
how does MHajduk display upside-down digits?
No, a PC could not? Unless it has upside-down options?
So, how do code-breaker spooks work? Do they have a huge library of every language ever written, Chinese, Japanese, Koren, Arabic etc scripts?
The first replier... keep taking the medication please
13 Jan 2014, 20:31
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
Well, my computer surely didn't solve it. I asked the question in a very clear voice, and it didn't even respond.
13 Jan 2014, 21:22
typedef

Joined: 25 Jul 2010
Posts: 2913
Location: 0x77760000
typedef
tthsqe wrote:
Well, my computer surely didn't solve it. I asked the question in a very clear voice, and it didn't even respond.

Yes. And remember that computers do what they are told. If they can't process a request, it' because they were never made to do so.
13 Jan 2014, 22:51
matefkr

Joined: 02 Sep 2007
Posts: 1291
Location: Ukraine, Beregovo
matefkr
I still give too much of a fuck about it.
14 Jan 2014, 00:37
matefkr

Joined: 02 Sep 2007
Posts: 1291
Location: Ukraine, Beregovo
matefkr
tthsqe is approaching it the right way.
14 Jan 2014, 00:39
HaHaAnonymous

Joined: 02 Dec 2012
Posts: 1180
Location: Unknown
HaHaAnonymous
[ Post removed by author. ]

Last edited by HaHaAnonymous on 28 Feb 2015, 18:36; edited 1 time in total
14 Jan 2014, 01:05
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