Question 97
Let $2^{-n_1} + 2^{-n_2} + \dots + 2^{-n_k} + \dots$, where $1 \le n_1 \lt n_2 \lt \dots \lt n_k \lt \dots$, be the binary expansion of $(\sqrt{5}-1)/2$. Prove that $n_k \le 2^{k-1}-2$ for all integers $k \ge 4$.
*Amer. Math. Monthly*
*Amer. Math. Monthly*