Question 66
A grasshopper is jumping along the set $\mathbb{Z}$ of integers. He starts at the origin; and for each jump, he may decide whether to jump to the left or to the right. For each $n \in \mathbb{N}_0$, the $n$-th jump has length $n^2$.
Prove or disprove that for each $k \in \mathbb{Z}$ the grasshopper can arrive at $k$ starting from origin.
Prove or disprove that for each $k \in \mathbb{Z}$ the grasshopper can arrive at $k$ starting from origin.