[seqfan] Re: parametric integer functions with GCD[f1,f2,f3]=1
Artur
grafix at csl.pl
Tue Nov 11 22:11:53 CET 2008
Dear Seqfans,
e.g. 3 such polynomials are:
pol1 = 25 - 204 x + 468 x^2; pol2 = -7 - 12 x + 180 x^2; pol3=12 - 108
x + 216 x^2;
and GCD[pol1, pol2] == 1 && GCD[pol1, pol3] == 1 &&
GCD[pol2, pol3] == 1 for every natural number x
Do you know another such pol1,pol2,pol3?
Best wishes
Artur
Edwin Clark pisze:
>
> Arthur,
>
> How about p[n],p[n+1],p[n+2]? ... where p[n] is the nth prime.
>
> Edwin
>
>
> On Tue, 11 Nov 2008, Artur wrote:
>
>> Sorry, but I was do mistake
>> my problem should by GCD[a,b]=1&GCD[a,c]=1&GCD[b,c]=1
>>
>> gcd(n,n+1,n^2) = 1
>> gcd(n,n+1,n-1) = 1
>>
>>
>> Edwin Clark pisze:
>>>
>>> Artur,
>>>
>>> As I understand it gcd(a,b,c) is the largest integer d that divides
>>> a, b and c. Thus if gcd(a,b) = 1 then for all c, gcd(a,b,c) = 1.
>>>
>>> So for example for all n
>>>
>>> gcd(n,n+1,n^2) = 1
>>> gcd(n,n+1,n-1) = 1
>>> gcd(n,n+1,n^3+n^2+floor(n/10)) = 1
>>> etc..
>>>
>>> Best wishes,
>>>
>>> Edwin
>>>
>>>
>>>
>>>
>>> On Tue, 11 Nov 2008, Artur wrote:
>>>
>>>> Dear Edwin,
>>>> What you mean "anything" anythink have to be function of n and
>>>> doesn't existed such n
>>>> that GCD(n,n-1,anything(n))<>1 or GCD(n,n+1,anything(n))
>>>> I'm looking for such anything if you know let me know.
>>>> Best wishes
>>>> Artur
>>>>
>>>> Edwin Clark pisze:
>>>>> On Tue, 11 Nov 2008, Artur wrote:
>>>>>
>>>>>> Dear Seqfans,
>>>>>>
>>>>>> I'm looking for one (or more) parametric 3 integer functions such
>>>>>> that
>>>>>> GCD[f1,f2,f3]=1 for every value of parameter
>>>>>> Example of these is e.g. :
>>>>>> GCD[Prime[x]^2+(Prime[x]-1)^2, Prime[x]^2-(Prime[x]-1)^2, 2
>>>>>> Prime[x]^2
>>>>>> (Prime[x]-1)]=1
>>>>>> I'm looking for another. If sombody know these let me know!
>>>>>>
>>>>>
>>>>>
>>>>> How about GCD(n,n-1,anything) or GCD(n,n+1,anything)? Or am I missing
>>>>> something.
>>>>>
>>>>> --Edwin
>>>>>
>>>>>
>>>>>
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>>>>> The message was checked by ESET NOD32 Antivirus.
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>>>>>
>>>>>
>>>>
>>>
>>>
>>> __________ Information from ESET NOD32 Antivirus, version of virus
>>> signature database 3603 (20081111) __________
>>>
>>> The message was checked by ESET NOD32 Antivirus.
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>>
>
>
> __________ Information from ESET NOD32 Antivirus, version of virus
> signature database 3603 (20081111) __________
>
> The message was checked by ESET NOD32 Antivirus.
>
> http://www.eset.com
>
>
>
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