## Taken from MIT's OpenCourseWare site for Discrete Math:

We deﬁne the following recurrence for $n ≥ 0$:$$T_{n+2} = T_{n+1} + 2T_{n}$$ where, $T_{0} = T_{1} = 1$(a) Prove by induction that: $T_{n}$ is odd for $n ≥ 0.$

You do not need to solve the recurrence for this.

(b) Prove by induction that: $$\gcd(T_{n+1}, T_{n}) = 1 \qquad\forall n ≥ 0.$$ You may assume that $T_{n}$ is odd for all $n$.

You do not need to solve the recurrence for this.