Recursions in Recursions - 2
Algebra
Level
4
\[ { \begin{eqnarray} a_{n} & =& 2a_{n-1} + 3 \\ b_{n} &=& b_{n-1} + b_{n-2} \\ \end{eqnarray} } \]
For a positive integer \(n\), consider the two recurrence relations above subjected to the conditions \(a_1 = 0\) and \(b_{1} = b_{2} = 1 \).
If the value of the expression \(\big(a_{b_{2015}} + 3\big)\big(a_{b_{2016}} + 3\big)\) can be expressed as \(p^{b_{q}} \frac{r}{s}\), where \(b_{q}\) is one of the terms in the recurrence relations sequence above and \((p, r)\) and \((r, s)\) are pairwise coprime integers.
Find the value of \((p+q+r+s) \bmod {673}\).
by
Surya Prakash