MathDB

The Fibonacci sequence is defined by F_1 \equal{} F_2 \equal{} 1 and F_{n\plus{}1} \equal{} F_n \plus{}F_{n\minus{}1} for

n > 1

. Let f(x) \equal{} 1985x^2 \plus{} 1956x \plus{} 1960. Prove that there exist infinitely many natural numbers

n

for which

f(F_n)

is divisible by

1989

. Does there exist

n

for which f(F_n) \plus{} 2 is divisible by

1989

Problem Statement