5 Dec
2009
5 Dec
'09
1:12 p.m.
On Sat, 5 Dec 2009, Eugene Salamin wrote:
Definition: A polynomial p(x) with rational coefficients is said to be "almost integer" if p(n) is an integer for all integers n. Example: x(x+1)/2.
It appears that such polynomials have been considered previously under the name "integer polynomials". It is interesting that they form a free abelian group with basis: t(t - 1)...(t - k + 1)/k!, k = 0,1,2,... according to: http://en.wikipedia.org/wiki/Integer-valued_polynomial I encounted them recently when I learned of "Schinzel's hypothesis H" http://en.wikipedia.org/wiki/Schinzel's_hypothesis_H.