Problem of the Month
Hint for Problem 2: November 2022

1. No hint given.

2. What is \(\phi+\dfrac{1}{\phi}\)?

3. No hint given.

4. One way to prove the first fact is to show that if there are two consecutive digits equal to \(1\), then there is a base \(\phi\) expansion with fewer non-zero digits. To prove the second fact, use the same idea as in the proof of the first fact, but in reverse.