Question 2
Consider the Fibonacci sequence $1,1,2,3,5,8,13,\ldots$. Put $f(n)=1985n^2+1956n+1960$.
(a) Prove that infinitely many terms $F$ of the Fibonacci sequence satisfy $1989\mid f(F)$.
(b) Does there exist a term $G$ of this sequence such that $1989\mid f(G)+2$?
(a) Prove that infinitely many terms $F$ of the Fibonacci sequence satisfy $1989\mid f(F)$.
(b) Does there exist a term $G$ of this sequence such that $1989\mid f(G)+2$?