Question 105
$a \gt k$ are two positive integers and two strictly increasing sequences $r_1 \lt r_2 \lt \dots \lt r_n$ and $s_1 \lt s_2 \lt \dots \lt s_n$ of positive integers have the following property,
$$
(a^{r_1} + k)(a^{r_2} + k)\dots(a^{r_n} + k) = (a^{s_1} + k)(a^{s_2} + k)\dots(a^{s_n} + k).
$$
Prove that these two sequences are equal, which means for each $1 \le i \le n$, $r_i = s_i$.
$$
(a^{r_1} + k)(a^{r_2} + k)\dots(a^{r_n} + k) = (a^{s_1} + k)(a^{s_2} + k)\dots(a^{s_n} + k).
$$
Prove that these two sequences are equal, which means for each $1 \le i \le n$, $r_i = s_i$.