Question: The Fibonacci numbers are defined by the recursion fn + 1 = fn + fn 1 , and the initial conditions that f 0 =

The Fibonacci numbers are defined by the recursion fn+1= fn + fn1, and the initial
conditions that f0= f1=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 (fn, fn+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.

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