The Fibonacci Numbers : 1,1,2,3,5,8,13,21,34... are defined by $\displaystyle a_0 =1, a_1 =1 $ and for n >2 by $\displaystyle a_n=a_{n-2}+ a_{n-1} $.

Show by induction that $\displaystyle a_{3n}$ is even.

base case: n=3 is 2, so it is even.

Assume $\displaystyle a_n=a_{n-2}+ a_{n-1} $ is even?

not sure how to do the induction step.

Thanks in advance