Let F_{n} denote the n^{th} Fibonacci number, with F_{0}=0, F_{1}=1 and F_{n}=F_{n-1}+F_{n-2} for n \geq 2. There exists a unique two digit prime p such that for all n, p \mid F_{n+100}+F_{n}. Find p.
Let F_{n} denote the n^{th} Fibonacci number, with F_{0}=0, F_{1}=1 and F_{n}=F_{n-1}+F_{n-2} for n \geq 2. There exists a unique two digit prime p such that for all n, p \mid F_{n+100}+F_{n}. Find p.