[seqfan] Re: parametric integer functions with GCD[f1,f2,f3]=1

[Robert Israel]

On Tue, 11 Nov 2008, Artur wrote:

> 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?

For any integer-valued polynomial p(x) try p(x), p(x)+1 and
p(x)^2 + p(x) + 1.

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada