Question 45
A polynomial $f(x)=\sum_{i=0}^{n} a_{i} x^{i}$ of degree $n$ or less is called happy if
(i) Each coefficient $a_{i}$ satisfies $0 \leq a_{i}\lt 1$;
(ii) $f(x)$ is an integer for all integers $x$.
Find the number of happy polynomials of degree $n$ or less.
(i) Each coefficient $a_{i}$ satisfies $0 \leq a_{i}\lt 1$;
(ii) $f(x)$ is an integer for all integers $x$.
Find the number of happy polynomials of degree $n$ or less.