Number Theory: Consecutive Fibonacci numbers are Relatively Prime: give a typed answer please
The Fibonacci numbers are defined by the recursion $f_{n+1} = f_n + f_{n-1}$, and the initial conditions that $f_0 = f_1 = 1$. The first few Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .
They are named after Fibonacci (1180-1228), aka Leonardo of Pisa.
Prove that $(f_n, f_{n+1}) = 1$. Your proof, naturally, will make use of the definition of the Fibonacci numbers. And, while it may not be absolutely necessary, your proof will probably be better if you use induction.