Question 74
Let $a$ and $b$ be integers and $k$ be a positive integer. Prove that if $x$ and $y$ are consecutive integers such that
$$
a^{k} x - b^{k} y = a - b
$$
then $|a-b|$ is a perfect $k$-th power.
$$
a^{k} x - b^{k} y = a - b
$$
then $|a-b|$ is a perfect $k$-th power.