solve recurrence relation $a_{n+2}=(a_{n+1}+1)/a_n$

Let $a_1$ = 2015, $a_2$=2016. Find $a_{2017}$, given $a_{n+2}=(a_{n+1}+1)/a_n$I have found the 2 roots of the characteristic equation $x^2-x-1=0$ :$r_1 = ((1+\sqrt{5})/2)^n$ , $r_2 = ((1-\sqrt{5})/2)^n$Then I have used a calculator to find that the coefficients a and b are -57.418 and 56.7999 respectively. However every calculator treats raising to the power of 2017 as an error. Where did I go wrong?