# Proof Ideas - Strong Induction, Pascal's Triangle and Fibonacci Numbers

I'm looking for attributes/characteristics/properties to prove about Pascal's Triangle or the Fibonacci numbers. Preferably something that requires a strong induction proof that is on the same level as proving things such as the sum of the elements in the nth row of Pascal's triangle is $$2^n$$. Simple induction proof ideas are also fine.

• How about Pascal's triangle and the Fibonacci numbers? Try proving that $F_{n+1} = \sum_{k \ge 0} {n-k \choose k}$. – Qiaochu Yuan Dec 5 '18 at 23:45
• The known properties of Pascal's triangle, and of the Fibonacci sequence, that can be proved by induction, can each fill a library. – DanielWainfleet Dec 6 '18 at 9:11