Question 7
(GRE 2) Let $f(0)=f(1)=0$ and
$$f(n+2)=4^{n+2}f(n+1)-16^{n+1}f(n)+n\cdot2^{n^2},\qquad n=0,1,2,3,\ldots.$$
Show that the numbers $f(1989),f(1990),f(1991)$ are divisible by 13.
$$f(n+2)=4^{n+2}f(n+1)-16^{n+1}f(n)+n\cdot2^{n^2},\qquad n=0,1,2,3,\ldots.$$
Show that the numbers $f(1989),f(1990),f(1991)$ are divisible by 13.