Let f(0) \equal{} f(1) \equal{} 0 and
f(n\plus{}2) \equal{} 4^{n\plus{}2} \cdot f(n\plus{}1) \minus{} 16^{n\plus{}1} \cdot f(n) \plus{} n \cdot 2^{n^2}, n \equal{} 0, 1, 2, \ldots
Show that the numbers f(1989),f(1990),f(1991) are divisible by 13. algebrapolynomialarithmetic sequencenumber theoryfunctional equationDivisibilityIMO Shortlist