Problem 2. (10 points) a. Recall the Fibonacci numbers: Find the simplest possible expression for gcd(F,Fn-1),n2 1. Prove the validity of your answer. (Hint: Calculate the gcd by hand for a few small values; then formulate and prove your hypothesis.) b. The numbers a, b, c are pairwise relative prime if gcd(a, b) gcd(b,c) -gcd(a, c)-1 Is it true that three consecutive Fibonacci numbers are always pairwise relatively prime? Prove your